The nonlinear dynamic characteristics of a two-peak discrete chaotic system are studied.Through the study of the nonlinear dy‐namic behavior of the system,it is found that with the change of the system parameters,the...The nonlinear dynamic characteristics of a two-peak discrete chaotic system are studied.Through the study of the nonlinear dy‐namic behavior of the system,it is found that with the change of the system parameters,the system starts from a chaotic state,and then goes through intermittent chaos,stable region,period-doubling bifurcation to a chaotic state again.The systems critical conditions and pro‐cess to generate intermittent chaos are analyzed.The feedback control method sets linear and nonlinear controllers for the system to control the chaos.By adjusting the value of control parameters,the intermittent chaos can be delayed or disappear,and the stability region and period-doubling bifurcation process of the system can be expanded.Both linear controllers and nonlinear controllers have the same control effect.The numerical simulation analysis verifies the correctness of the theoretical analysis.展开更多
The Industry 4.0 revolution is characterized by distributed infrastructures where data must be continuously communicated between hardware nodes and cloud servers.Specific lightweight cryptosystems are needed to protec...The Industry 4.0 revolution is characterized by distributed infrastructures where data must be continuously communicated between hardware nodes and cloud servers.Specific lightweight cryptosystems are needed to protect those links,as the hardware node tends to be resource-constrained.Then Pseudo Random Number Generators are employed to produce random keys,whose final behavior depends on the initial seed.To guarantee good mathematical behavior,most key generators need an unpredictable voltage signal as input.However,physical signals evolve slowly and have a significant autocorrelation,so they do not have enough entropy to support highrandomness seeds.Then,electronic mechanisms to generate those high-entropy signals artificially are required.This paper proposes a robust hyperchaotic circuit to obtain such unpredictable electric signals.The circuit is based on a hyperchaotic dynamic system,showing a large catalog of structures,four different secret parameters,and producing four high entropy voltage signals.Synchronization schemes for the correct secret key calculation and distribution among all remote communicating modules are also analyzed and discussed.Security risks and intruder and attacker models for the proposed solution are explored,too.An experimental validation based on circuit simulations and a real hardware implementation is provided.The results show that the random properties of PRNG improved by up to 11%when seeds were calculated through the proposed circuit.展开更多
Traditional chaotic maps struggle with narrow chaotic ranges and inefficiencies,limiting their use for lightweight,secure image encryption in resource-constrained Wireless Sensor Networks(WSNs).We propose the SPCM,a n...Traditional chaotic maps struggle with narrow chaotic ranges and inefficiencies,limiting their use for lightweight,secure image encryption in resource-constrained Wireless Sensor Networks(WSNs).We propose the SPCM,a novel one-dimensional discontinuous chaotic system integrating polynomial and sine functions,leveraging a piecewise function to achieve a broad chaotic range()and a high Lyapunov exponent(5.04).Validated through nine benchmarks,including standard randomness tests,Diehard tests,and Shannon entropy(3.883),SPCM demonstrates superior randomness and high sensitivity to initial conditions.Applied to image encryption,SPCM achieves 0.152582 s(39%faster than some techniques)and 433.42 KB/s throughput(134%higher than some techniques),setting new benchmarks for chaotic map-based methods in WSNs.Chaos-based permutation and exclusive or(XOR)diffusion yield near-zero correlation in encrypted images,ensuring strong resistance to Statistical Attacks(SA)and accurate recovery.SPCM also exhibits a strong avalanche effect(bit difference),making it an efficient,secure solution for WSNs in domains like healthcare and smart cities.展开更多
Memristor chaotic research has become a hotspot in the academic world.However,there is little exploration combining memristor and stochastic resonance,and the correlation research between chaos and stochastic resonanc...Memristor chaotic research has become a hotspot in the academic world.However,there is little exploration combining memristor and stochastic resonance,and the correlation research between chaos and stochastic resonance is still in the preliminary stage.In this paper,we focus on the stochastic resonance induced by memristor chaos,which enhances the dynamics of chaotic systems through the introduction of memristor and induces memristor stochastic resonance under certain conditions.First,the memristor chaos model is constructed,and the memristor stochastic resonance model is constructed by adjusting the parameters of the memristor chaos model.Second,the combination of dynamic analysis and experimental verification is used to analyze the memristor stochastic resonance and to investigate the trend of the output signal of the system under different amplitudes of the input signal.Finally,the practicality and reliability of the constructed model are further verified through the design and testing of the analog circuit,which provides strong support for the practical application of the memristor chaos-induced stochastic resonance model.展开更多
We investigate the chaotic and regular spatial structures of Bose–Einstein condensates(BECs)with a spatially modulated atom-atom interaction and without an external trapping potential.A BEC with a spatially modulated...We investigate the chaotic and regular spatial structures of Bose–Einstein condensates(BECs)with a spatially modulated atom-atom interaction and without an external trapping potential.A BEC with a spatially modulated atom-atom interaction is equivalent to being constrained by a nonlinear optical lattice.Theoretical analyses show the existence of a steady atomic current in the BEC with a spatially varying phase.Under perturbative conditions,the Melnikov chaos criteria of BECs with a spatially varying phase and a constant one are theoretically obtained,respectively.When the perturbative conditions cannot be satisfied,for a repulsive BEC with a spatially varying phase,numerical simulations demonstrate that changing the initial condition can eliminate the chaotic spatial structure and then the system transitions into a biperiodic spatial structure.Increasing the chemical potential can result in a transition from the biperiodic spatial structure to a single-periodic spatial structure.For an attractive BEC with a spatially varying phase,numerical simulations show that decreasing the chemical potential can lead to a high atomic density,but when the wave number of the laser inducing the optical Feshbach resonance exceeds a critical value,the atomic density falls back to a finite range.Regardless of whether the BEC has a spatially varying phase or a constant one,modulating the laser wave number can effectively suppress the chaotic spatial structure in the BEC and then force it into a regular spatial structure.展开更多
This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging...This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging the two movable mirrors.We examine the chaotic dynamics under the influence of both single and bichromatic laser fields.The single laser field represents a system driven exclusively by the pump field,whereas the bichromatic field represents simultaneous driving by both the pump and probe fields.In addition to conventional chaos-inducing methods through parameter variations,we demonstrate that increasing the Coulomb coupling strength enhances the system’s nonlinearity and induces chaotic behavior.Furthermore,we propose several strategies for generating and controlling chaos,while also identifying the parameter ranges necessary for the resonance of the two mechanical oscillators.Interestingly,when adjusting the driving power in a system driven solely by the pump field,we unexpectedly observe the emergence of high-order sidebands.These findings contribute to the development of chaotic behavior in future cavity optomechanical systems and provide a theoretical basis for applications in physical random number generation and secure communication.展开更多
Hydro-pneumatic near-zero frequency(NZF)vibration isolators have better performance at isolating vibration with low frequencies and heavy loadings when the nonlinear fluidic damping is introduced and the pressurized g...Hydro-pneumatic near-zero frequency(NZF)vibration isolators have better performance at isolating vibration with low frequencies and heavy loadings when the nonlinear fluidic damping is introduced and the pressurized gas pressure is properly adjusted.The nonlinear characteristics of such devices make their corresponding dynamic research involve chaotic dynamics.Chaos may bring negative influence and disorder to the structure and low-frequency working efficiency of isolators,which makes it necessary to clarify and control the threshold ranges for chaos generation in advance.In this work,the chaotic characteristics for a class of hydro-pneumatic NZF vibration isolators under dry friction,harmonic,and environmental noise excitations are analyzed by the analytical and numerical methods.The parameter ranges for the generation of chaos are obtained by the classical and random Melnikov methods.The chaotic characteristics and thresholds of the parameters in the systems with or without noise excitation are discussed and described.The analytical solutions and the influence of noise and harmonic excitation about chaos are tested and further analyzed through many numerical simulations.The results show that chaos in the system can be induced or inhibited with the adjustment of the magnitudes of harmonic excitation and noise intensity.展开更多
In this paper,we investigate the distinctions between dynamical quantum chaotic systems and random models from the perspective of observable properties,particularly focusing on the eigenstate thermalization hypothesis...In this paper,we investigate the distinctions between dynamical quantum chaotic systems and random models from the perspective of observable properties,particularly focusing on the eigenstate thermalization hypothesis(ETH).Through numerical simulations,we find that for dynamical systems,the envelope function of off-diagonal elements of observables exhibits an exponential decay at largeΔE,while for randomized models,it tends to be flat.We demonstrate that the correlations of chaotic eigenstates,originating from the delicate structures of Hamiltonians,play a crucial role in the non-trivial structure of the envelope function.Furthermore,we analyze the numerical results from the perspective of the dynamical group elements in Hamiltonians.Our findings highlight the importance of correlations in physical chaotic systems and provide insights into the deviations from random matrix theory(RMT)predictions.These understandings offer valuable directions for future research.展开更多
Understanding neural dynamics is a central topic in machine learning,non-linear physics,and neuroscience.However,the dynamics are non-linear,stochastic and particularly non-gradient,i.e.,the driving force cannot be wr...Understanding neural dynamics is a central topic in machine learning,non-linear physics,and neuroscience.However,the dynamics are non-linear,stochastic and particularly non-gradient,i.e.,the driving force cannot be written as the gradient of a potential.These features make analytic studies very challenging.The common tool is the path integral approach or dynamical mean-field theory.Still,the drawback is that one has to solve the integro-differential or dynamical mean-field equations,which is computationally expensive and has no closed-form solutions in general.From the associated Fokker-Planck equation,the steady-state solution is generally unknown.Here,we treat searching for the fixed points as an optimization problem,and construct an approximate potential related to the speed of the dynamics,and find that searching for the ground state of this potential is equivalent to running approximate stochastic gradient dynamics or Langevin dynamics.Only in the zero temperature limit,can the distribution of the original fixed points be achieved.The resultant stationary state of the dynamics exactly follows the canonical Boltzmann measure.Within this framework,the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method,which leads naturally to order parameters for the non-equilibrium steady states.Our theory reproduces the well-known result of edge-of-chaos.Furthermore,the order parameters characterizing the continuous transition are derived,and the order parameters are explained as fluctuations and responses of the steady states.Our method thus opens the door to analytically studying the fixed-point landscape of the deterministic or stochastic high dimensional dynamics.展开更多
Aquila Optimizer(AO)is a recently proposed population-based optimization technique inspired by Aquila’s behavior in catching prey.AO is applied in various applications and its numerous variants were proposed in the l...Aquila Optimizer(AO)is a recently proposed population-based optimization technique inspired by Aquila’s behavior in catching prey.AO is applied in various applications and its numerous variants were proposed in the literature.However,chaos theory has not been extensively investigated in AO.Moreover,it is still not applied in the parameter estimation of electro-hydraulic systems.In this work,ten well-defined chaotic maps were integrated into a narrowed exploitation of AO for the development of a robust chaotic optimization technique.An extensive investigation of twenty-three mathematical benchmarks and ten IEEE Congress on Evolutionary Computation(CEC)functions shows that chaotic Aquila optimization techniques perform better than the baseline technique.The investigation is further conducted on parameter estimation of an electro-hydraulic control system,which is performed on various noise levels and shows that the proposed chaotic AO with Piecewise map(CAO6)achieves the best fitness values of and at noise levels and respectively.Friedman test 2.873E-05,1.014E-04,8.728E-031.300E-03,1.300E-02,1.300E-01,for repeated measures,computational analysis,and Taguchi test reflect the superiority of CAO6 against the state of the arts,demonstrating its potential for addressing various engineering optimization problems.However,the sensitivity to parameter tuning may limit its direct application to complex optimization scenarios.展开更多
This paper presents a high-security medical image encryption method that leverages a novel and robust sine-cosine map.The map demonstrates remarkable chaotic dynamics over a wide range of parameters.We employ nonlinea...This paper presents a high-security medical image encryption method that leverages a novel and robust sine-cosine map.The map demonstrates remarkable chaotic dynamics over a wide range of parameters.We employ nonlinear analytical tools to thoroughly investigate the dynamics of the chaotic map,which allows us to select optimal parameter configurations for the encryption process.Our findings indicate that the proposed sine-cosine map is capable of generating a rich variety of chaotic attractors,an essential characteristic for effective encryption.The encryption technique is based on bit-plane decomposition,wherein a plain image is divided into distinct bit planes.These planes are organized into two matrices:one containing the most significant bit planes and the other housing the least significant ones.The subsequent phases of chaotic confusion and diffusion utilize these matrices to enhance security.An auxiliary matrix is then generated,comprising the combined bit planes that yield the final encrypted image.Experimental results demonstrate that our proposed technique achieves a commendable level of security for safeguarding sensitive patient information in medical images.As a result,image quality is evaluated using the Structural Similarity Index(SSIM),yielding values close to zero for encrypted images and approaching one for decrypted images.Additionally,the entropy values of the encrypted images are near 8,with a Number of Pixel Change Rate(NPCR)and Unified Average Change Intensity(UACI)exceeding 99.50%and 33%,respectively.Furthermore,quantitative assessments of occlusion attacks,along with comparisons to leading algorithms,validate the integrity and efficacy of our medical image encryption approach.展开更多
Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting ...Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting multi-hazard dynamic responses to super high-rise structures has significant engineering and scientific value. This study performed a parametric global sensitivity analysis (GSA) for multi-hazard dynamic response prediction of super high-rise structures using the multiple-degree-of-freedom shear (MFS) model. Polynomial chaos Kriging (PCK) was introduced to build a surrogate model that allowed GSA to be combined with Sobol’ indices. Monte Carlo simulation (MCS) is also conducted for the comparison to verify the accuracy and efficiency of the PCK method. Parametric sensitivity analysis is performed for a wide range of aleatory uncertainty (intensities of coupled multi-hazard), epistemic uncertainty (bending stiffness, k_(m);shear stiffness, kq;density, ρ;and damping ratio, ξ), probability distribution types, and coefficients of variation. The results indicate that epistemic uncertainty parameters, k_(m), ρ, and ξ dramatically affect the multi-hazard dynamic responses of super high-rise structures;in addition, Sobol’ indices between the normal and lognormal distributions are insignificant, while the variation levels have remarkably influenced the sensitivity indices.展开更多
In this paper,we investigate the propagation of chaos for solutions to the Liouville equation derived from the Linear-Formation particle model.By imposing certain conditions,we derive the rate of convergence between t...In this paper,we investigate the propagation of chaos for solutions to the Liouville equation derived from the Linear-Formation particle model.By imposing certain conditions,we derive the rate of convergence between the k-tensor product f_(t)^(■k)of the solution to be Linear-Formation kinetic equation and the k-marginal f_(N,k)^(t)of the solution to the Liouville equation corresponding to the Linear-Formation particle model.Specifically,the following estimate holds in terms of p-Wasserstein(1≤p<∞)distance W_(p)^(p)(f_(t)^(■k),f_(N,k)^(t))≤C_(1)k/N^(min(p/2,1))(1+t^(p))e^(C_(2)^(t)),1≤k≤N.展开更多
The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break...The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break then cause chaos in severe cases.In this paper,the stability of solitary waves and chaos suppression in fiber-reinforced compressible hyperelastic cylindrical shells are investigated,and sufficient conditions for chaos generation as well as chaos suppression in cylindrical shells are provided.Under the radial periodic load and structural damping,the traveling wave equation describing the single radial symmetric motion of the cylindrical shell is obtained by using the variational principle and traveling wave method.By employing the bifurcation theory of dynamical systems,the parameter space for the appearance of peak solitary waves,valley solitary waves,and periodic waves in an undisturbed system is determined.The sufficient conditions for chaos generation are derived by the Melnikov method.It is found that the disturbed system leads to chaotic motions in the form of period-doubling bifurcation.Furthermore,a second weak periodic disturbance is applied as the non-feedback control input to suppress chaos,and the initial phase difference serves as the control parameter.According to the Melnikov function,the sufficient conditions for the second excitation amplitude and initial phase difference to suppress chaos are determined.The chaotic motions can be successfully converted to some regular motions by weak periodic perturbations.The results of theoretical analyses are compared with numerical simulation,and they are in good agreement.This paper extends the research scope of nonlinear elastic dynamics,and provides a strategy for controlling chaotic responses of hyperelastic structures.展开更多
We experimentally analyze the effect of the optical power on the time delay signature identification and the random bit generation in chaotic semiconductor laser with optical feedback.Due to the inevitable noise durin...We experimentally analyze the effect of the optical power on the time delay signature identification and the random bit generation in chaotic semiconductor laser with optical feedback.Due to the inevitable noise during the photoelectric detection and analog-digital conversion,the varying of output optical power would change the signal to noise ratio,then impact time delay signature identification and the random bit generation.Our results show that,when the optical power is less than-14 dBm,with the decreasing of the optical power,the actual identified time delay signature degrades and the entropy of the chaotic signal increases.Moreover,the extracted random bit sequence with lower optical power is more easily pass through the randomness testing.展开更多
Model-free,data-driven prediction of chaotic motions is a long-standing challenge in nonlinear science.Stimulated by the recent progress in machine learning,considerable attention has been given to the inference of ch...Model-free,data-driven prediction of chaotic motions is a long-standing challenge in nonlinear science.Stimulated by the recent progress in machine learning,considerable attention has been given to the inference of chaos by the technique of reservoir computing(RC).In particular,by incorporating a parameter-control channel into the standard RC,it is demonstrated that the machine is able to not only replicate the dynamics of the training states,but also infer new dynamics not included in the training set.The new machine-learning scheme,termed parameter-aware RC,opens up new avenues for data-based analysis of chaotic systems,and holds promise for predicting and controlling many real-world complex systems.Here,using typical chaotic systems as examples,we give a comprehensive introduction to this powerful machine-learning technique,including the algorithm,the implementation,the performance,and the open questions calling for further studies.展开更多
Using the Melnikov method,the phenomenon of thermal chaos under periodic perturbation in the extended phase space of the modified thermodynamics of Kerr-AdS black holes is investigated.On the(P,v)section in the extend...Using the Melnikov method,the phenomenon of thermal chaos under periodic perturbation in the extended phase space of the modified thermodynamics of Kerr-AdS black holes is investigated.On the(P,v)section in the extended phase space,it is shown that temporal chaos will appear in the unstable spinodal region when the perturbation amplitude is larger than critical value δ_(c)^(Pv).We findδ_(c)^(Pv) is monotonically decreasing with respect to the angular momentum parameter a,which implies a large a leads to chaotic behavior more easily under time-periodic thermal perturbation.Similarly,on the(Ω_(H),J)section,we show there exists a critical value δ_(c)^(ΩJ) which depends on the cosmological parameter l=√-3/Λ.When the perturbation amplitude exceeds δ_(c)^(ΩJ),temporal chaos occurs.As l increases,chaos becomes easier.For spatial perturbation,chaos always exists irrespective of perturbation amplitude in both the(P,v)section and(Ω_(H),J)section.展开更多
As one of the famous effects in the quantum Rabi model(QRM),Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts,such as quantum collapse and revival effect...As one of the famous effects in the quantum Rabi model(QRM),Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts,such as quantum collapse and revival effects.In this paper,we focus on studying the long-time quantum signatures of chaos in the large atom-light frequency ratios of the Rabi model.It is shown that the saturated values of the entanglement entropy for initial states located in chaotic sea are higher than that in the regular regions,and the Husimi Q function are more dispersed in phase space.Moreover,we observed that the long-time average entanglement entropy and spin variance correspond well with the semiclassical phase space.Our results imply that the correspondence principle is not invalidated by quantum collapse and revival effects in the large atom-light frequency ratios Rabi model.展开更多
This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-...This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.展开更多
基金Supported by the Guiding Project of Science and Technology Research Plan of Hubei Provincial Department of Education(B2022458)。
文摘The nonlinear dynamic characteristics of a two-peak discrete chaotic system are studied.Through the study of the nonlinear dy‐namic behavior of the system,it is found that with the change of the system parameters,the system starts from a chaotic state,and then goes through intermittent chaos,stable region,period-doubling bifurcation to a chaotic state again.The systems critical conditions and pro‐cess to generate intermittent chaos are analyzed.The feedback control method sets linear and nonlinear controllers for the system to control the chaos.By adjusting the value of control parameters,the intermittent chaos can be delayed or disappear,and the stability region and period-doubling bifurcation process of the system can be expanded.Both linear controllers and nonlinear controllers have the same control effect.The numerical simulation analysis verifies the correctness of the theoretical analysis.
基金supported by Comunidad de Madrid within the framework of the Multiannual Agreement with Universidad Politecnica de Madrid to encourage research by young doctors(PRINCE).
文摘The Industry 4.0 revolution is characterized by distributed infrastructures where data must be continuously communicated between hardware nodes and cloud servers.Specific lightweight cryptosystems are needed to protect those links,as the hardware node tends to be resource-constrained.Then Pseudo Random Number Generators are employed to produce random keys,whose final behavior depends on the initial seed.To guarantee good mathematical behavior,most key generators need an unpredictable voltage signal as input.However,physical signals evolve slowly and have a significant autocorrelation,so they do not have enough entropy to support highrandomness seeds.Then,electronic mechanisms to generate those high-entropy signals artificially are required.This paper proposes a robust hyperchaotic circuit to obtain such unpredictable electric signals.The circuit is based on a hyperchaotic dynamic system,showing a large catalog of structures,four different secret parameters,and producing four high entropy voltage signals.Synchronization schemes for the correct secret key calculation and distribution among all remote communicating modules are also analyzed and discussed.Security risks and intruder and attacker models for the proposed solution are explored,too.An experimental validation based on circuit simulations and a real hardware implementation is provided.The results show that the random properties of PRNG improved by up to 11%when seeds were calculated through the proposed circuit.
基金supported by the National Research Foundation of Korea(NRF)grant funded by the Korean government Ministry of Science and ICT(MIST)(RS-2022-00165225).
文摘Traditional chaotic maps struggle with narrow chaotic ranges and inefficiencies,limiting their use for lightweight,secure image encryption in resource-constrained Wireless Sensor Networks(WSNs).We propose the SPCM,a novel one-dimensional discontinuous chaotic system integrating polynomial and sine functions,leveraging a piecewise function to achieve a broad chaotic range()and a high Lyapunov exponent(5.04).Validated through nine benchmarks,including standard randomness tests,Diehard tests,and Shannon entropy(3.883),SPCM demonstrates superior randomness and high sensitivity to initial conditions.Applied to image encryption,SPCM achieves 0.152582 s(39%faster than some techniques)and 433.42 KB/s throughput(134%higher than some techniques),setting new benchmarks for chaotic map-based methods in WSNs.Chaos-based permutation and exclusive or(XOR)diffusion yield near-zero correlation in encrypted images,ensuring strong resistance to Statistical Attacks(SA)and accurate recovery.SPCM also exhibits a strong avalanche effect(bit difference),making it an efficient,secure solution for WSNs in domains like healthcare and smart cities.
文摘Memristor chaotic research has become a hotspot in the academic world.However,there is little exploration combining memristor and stochastic resonance,and the correlation research between chaos and stochastic resonance is still in the preliminary stage.In this paper,we focus on the stochastic resonance induced by memristor chaos,which enhances the dynamics of chaotic systems through the introduction of memristor and induces memristor stochastic resonance under certain conditions.First,the memristor chaos model is constructed,and the memristor stochastic resonance model is constructed by adjusting the parameters of the memristor chaos model.Second,the combination of dynamic analysis and experimental verification is used to analyze the memristor stochastic resonance and to investigate the trend of the output signal of the system under different amplitudes of the input signal.Finally,the practicality and reliability of the constructed model are further verified through the design and testing of the analog circuit,which provides strong support for the practical application of the memristor chaos-induced stochastic resonance model.
基金Projects supported by the Natural Science Foundation of Hunan Province(2016JJ6020)the Scientific Research Fund of Hunan Provincial Education Department(18A436)the Scientific Research Fund of Hunan First normal University(XYS13N16)。
文摘We investigate the chaotic and regular spatial structures of Bose–Einstein condensates(BECs)with a spatially modulated atom-atom interaction and without an external trapping potential.A BEC with a spatially modulated atom-atom interaction is equivalent to being constrained by a nonlinear optical lattice.Theoretical analyses show the existence of a steady atomic current in the BEC with a spatially varying phase.Under perturbative conditions,the Melnikov chaos criteria of BECs with a spatially varying phase and a constant one are theoretically obtained,respectively.When the perturbative conditions cannot be satisfied,for a repulsive BEC with a spatially varying phase,numerical simulations demonstrate that changing the initial condition can eliminate the chaotic spatial structure and then the system transitions into a biperiodic spatial structure.Increasing the chemical potential can result in a transition from the biperiodic spatial structure to a single-periodic spatial structure.For an attractive BEC with a spatially varying phase,numerical simulations show that decreasing the chemical potential can lead to a high atomic density,but when the wave number of the laser inducing the optical Feshbach resonance exceeds a critical value,the atomic density falls back to a finite range.Regardless of whether the BEC has a spatially varying phase or a constant one,modulating the laser wave number can effectively suppress the chaotic spatial structure in the BEC and then force it into a regular spatial structure.
基金supported by Young Talents from Longyuan,Gansu Province(Liwei Liu),the Fundamental Research Funds for the Central Universities,Northwest Minzu University(Grant No.31920230134)Teaching Achievement Cultivation Project of Gansu Province Department of Education(Grant No.2022GSJXCGPY-46)+1 种基金Special research topic on curriculum and teaching materials for primary,secondary and higher schools,Gansu Province Department of Education(Grant No.GSJC-Y2024204)Quality improvement project for undergraduate talent training,Northwest Minzu University(Grant Nos.2024YBJG-04 and 2024FCTD-03).
文摘This study theoretically investigates chaos in a cavity optomechanical system with Coulomb coupling.The system consists of a Fabry-Pérot cavity with a movable mirror,where Coulomb interactions arise from charging the two movable mirrors.We examine the chaotic dynamics under the influence of both single and bichromatic laser fields.The single laser field represents a system driven exclusively by the pump field,whereas the bichromatic field represents simultaneous driving by both the pump and probe fields.In addition to conventional chaos-inducing methods through parameter variations,we demonstrate that increasing the Coulomb coupling strength enhances the system’s nonlinearity and induces chaotic behavior.Furthermore,we propose several strategies for generating and controlling chaos,while also identifying the parameter ranges necessary for the resonance of the two mechanical oscillators.Interestingly,when adjusting the driving power in a system driven solely by the pump field,we unexpectedly observe the emergence of high-order sidebands.These findings contribute to the development of chaotic behavior in future cavity optomechanical systems and provide a theoretical basis for applications in physical random number generation and secure communication.
基金Project supported by the National Natural Science Foundation of China(Nos.12172340 and12411530068)the Shenzhen Science and Technology Program(No.JCYJ20240813114012016)+2 种基金the High-Level Talent Introduction Plan of Guangzhou Citythe Fundamental Research Funds for the Central Universities-China University of Geosciences(Wuhan)(No.G1323524005)the Young Top-Notch Talent Cultivation Program of Hubei Province。
文摘Hydro-pneumatic near-zero frequency(NZF)vibration isolators have better performance at isolating vibration with low frequencies and heavy loadings when the nonlinear fluidic damping is introduced and the pressurized gas pressure is properly adjusted.The nonlinear characteristics of such devices make their corresponding dynamic research involve chaotic dynamics.Chaos may bring negative influence and disorder to the structure and low-frequency working efficiency of isolators,which makes it necessary to clarify and control the threshold ranges for chaos generation in advance.In this work,the chaotic characteristics for a class of hydro-pneumatic NZF vibration isolators under dry friction,harmonic,and environmental noise excitations are analyzed by the analytical and numerical methods.The parameter ranges for the generation of chaos are obtained by the classical and random Melnikov methods.The chaotic characteristics and thresholds of the parameters in the systems with or without noise excitation are discussed and described.The analytical solutions and the influence of noise and harmonic excitation about chaos are tested and further analyzed through many numerical simulations.The results show that chaos in the system can be induced or inhibited with the adjustment of the magnitudes of harmonic excitation and noise intensity.
基金partially supported by the Natural Science Foundation of China under Grant Nos.12175222,11535011,and 11775210support from Deutsche Forschungsgemeinschaft(DFG)under Grant No.531128043 and also under Grant Nos.397107022,397067869 and 397082825,within the DFG Research Unit FOR 2692,under Grant No.355031190。
文摘In this paper,we investigate the distinctions between dynamical quantum chaotic systems and random models from the perspective of observable properties,particularly focusing on the eigenstate thermalization hypothesis(ETH).Through numerical simulations,we find that for dynamical systems,the envelope function of off-diagonal elements of observables exhibits an exponential decay at largeΔE,while for randomized models,it tends to be flat.We demonstrate that the correlations of chaotic eigenstates,originating from the delicate structures of Hamiltonians,play a crucial role in the non-trivial structure of the envelope function.Furthermore,we analyze the numerical results from the perspective of the dynamical group elements in Hamiltonians.Our findings highlight the importance of correlations in physical chaotic systems and provide insights into the deviations from random matrix theory(RMT)predictions.These understandings offer valuable directions for future research.
基金supported by the National Natural Science Foundation of China under Grant No.12122515(HH)Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices(Grant No.2022B1212010008)Guangdong Basic and Applied Basic Research Foundation(Grant No.2023B1515040023)。
文摘Understanding neural dynamics is a central topic in machine learning,non-linear physics,and neuroscience.However,the dynamics are non-linear,stochastic and particularly non-gradient,i.e.,the driving force cannot be written as the gradient of a potential.These features make analytic studies very challenging.The common tool is the path integral approach or dynamical mean-field theory.Still,the drawback is that one has to solve the integro-differential or dynamical mean-field equations,which is computationally expensive and has no closed-form solutions in general.From the associated Fokker-Planck equation,the steady-state solution is generally unknown.Here,we treat searching for the fixed points as an optimization problem,and construct an approximate potential related to the speed of the dynamics,and find that searching for the ground state of this potential is equivalent to running approximate stochastic gradient dynamics or Langevin dynamics.Only in the zero temperature limit,can the distribution of the original fixed points be achieved.The resultant stationary state of the dynamics exactly follows the canonical Boltzmann measure.Within this framework,the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method,which leads naturally to order parameters for the non-equilibrium steady states.Our theory reproduces the well-known result of edge-of-chaos.Furthermore,the order parameters characterizing the continuous transition are derived,and the order parameters are explained as fluctuations and responses of the steady states.Our method thus opens the door to analytically studying the fixed-point landscape of the deterministic or stochastic high dimensional dynamics.
基金funded by Taif University,Saudi Arabia,Project No.(TU-DSPP-2024-52).
文摘Aquila Optimizer(AO)is a recently proposed population-based optimization technique inspired by Aquila’s behavior in catching prey.AO is applied in various applications and its numerous variants were proposed in the literature.However,chaos theory has not been extensively investigated in AO.Moreover,it is still not applied in the parameter estimation of electro-hydraulic systems.In this work,ten well-defined chaotic maps were integrated into a narrowed exploitation of AO for the development of a robust chaotic optimization technique.An extensive investigation of twenty-three mathematical benchmarks and ten IEEE Congress on Evolutionary Computation(CEC)functions shows that chaotic Aquila optimization techniques perform better than the baseline technique.The investigation is further conducted on parameter estimation of an electro-hydraulic control system,which is performed on various noise levels and shows that the proposed chaotic AO with Piecewise map(CAO6)achieves the best fitness values of and at noise levels and respectively.Friedman test 2.873E-05,1.014E-04,8.728E-031.300E-03,1.300E-02,1.300E-01,for repeated measures,computational analysis,and Taguchi test reflect the superiority of CAO6 against the state of the arts,demonstrating its potential for addressing various engineering optimization problems.However,the sensitivity to parameter tuning may limit its direct application to complex optimization scenarios.
文摘This paper presents a high-security medical image encryption method that leverages a novel and robust sine-cosine map.The map demonstrates remarkable chaotic dynamics over a wide range of parameters.We employ nonlinear analytical tools to thoroughly investigate the dynamics of the chaotic map,which allows us to select optimal parameter configurations for the encryption process.Our findings indicate that the proposed sine-cosine map is capable of generating a rich variety of chaotic attractors,an essential characteristic for effective encryption.The encryption technique is based on bit-plane decomposition,wherein a plain image is divided into distinct bit planes.These planes are organized into two matrices:one containing the most significant bit planes and the other housing the least significant ones.The subsequent phases of chaotic confusion and diffusion utilize these matrices to enhance security.An auxiliary matrix is then generated,comprising the combined bit planes that yield the final encrypted image.Experimental results demonstrate that our proposed technique achieves a commendable level of security for safeguarding sensitive patient information in medical images.As a result,image quality is evaluated using the Structural Similarity Index(SSIM),yielding values close to zero for encrypted images and approaching one for decrypted images.Additionally,the entropy values of the encrypted images are near 8,with a Number of Pixel Change Rate(NPCR)and Unified Average Change Intensity(UACI)exceeding 99.50%and 33%,respectively.Furthermore,quantitative assessments of occlusion attacks,along with comparisons to leading algorithms,validate the integrity and efficacy of our medical image encryption approach.
基金Dalian Municipal Natural Science Foundation under Grant No.2019RD01。
文摘Economic losses and catastrophic casualties may occur once super high-rise structures are struck by low-probability but high-consequence scenarios of concurrent earthquakes and winds. Therefore, accurately predicting multi-hazard dynamic responses to super high-rise structures has significant engineering and scientific value. This study performed a parametric global sensitivity analysis (GSA) for multi-hazard dynamic response prediction of super high-rise structures using the multiple-degree-of-freedom shear (MFS) model. Polynomial chaos Kriging (PCK) was introduced to build a surrogate model that allowed GSA to be combined with Sobol’ indices. Monte Carlo simulation (MCS) is also conducted for the comparison to verify the accuracy and efficiency of the PCK method. Parametric sensitivity analysis is performed for a wide range of aleatory uncertainty (intensities of coupled multi-hazard), epistemic uncertainty (bending stiffness, k_(m);shear stiffness, kq;density, ρ;and damping ratio, ξ), probability distribution types, and coefficients of variation. The results indicate that epistemic uncertainty parameters, k_(m), ρ, and ξ dramatically affect the multi-hazard dynamic responses of super high-rise structures;in addition, Sobol’ indices between the normal and lognormal distributions are insignificant, while the variation levels have remarkably influenced the sensitivity indices.
基金supported by the Natural Science Foundation of Hunan Province(2022JJ30655)the National Natural Science Foundation of China(12371180)the Training Program for Excellent Young Innovators of Changsha(kq2305046)。
文摘In this paper,we investigate the propagation of chaos for solutions to the Liouville equation derived from the Linear-Formation particle model.By imposing certain conditions,we derive the rate of convergence between the k-tensor product f_(t)^(■k)of the solution to be Linear-Formation kinetic equation and the k-marginal f_(N,k)^(t)of the solution to the Liouville equation corresponding to the Linear-Formation particle model.Specifically,the following estimate holds in terms of p-Wasserstein(1≤p<∞)distance W_(p)^(p)(f_(t)^(■k),f_(N,k)^(t))≤C_(1)k/N^(min(p/2,1))(1+t^(p))e^(C_(2)^(t)),1≤k≤N.
基金support from the National Natural Science Foundation of China(Nos.12102242 and 12172086)the Educational Foundation of Liaoning Province(No.JYTQN2023261)the Key R&D Program of Shandong Province of China(No.2022SFGC0801).
文摘The propagation of solitary waves in fiber-reinforced hyperelastic cylindrical shells holds tremendous potential for structural health monitoring.However,solitary waves under external forces are unstable,and may break then cause chaos in severe cases.In this paper,the stability of solitary waves and chaos suppression in fiber-reinforced compressible hyperelastic cylindrical shells are investigated,and sufficient conditions for chaos generation as well as chaos suppression in cylindrical shells are provided.Under the radial periodic load and structural damping,the traveling wave equation describing the single radial symmetric motion of the cylindrical shell is obtained by using the variational principle and traveling wave method.By employing the bifurcation theory of dynamical systems,the parameter space for the appearance of peak solitary waves,valley solitary waves,and periodic waves in an undisturbed system is determined.The sufficient conditions for chaos generation are derived by the Melnikov method.It is found that the disturbed system leads to chaotic motions in the form of period-doubling bifurcation.Furthermore,a second weak periodic disturbance is applied as the non-feedback control input to suppress chaos,and the initial phase difference serves as the control parameter.According to the Melnikov function,the sufficient conditions for the second excitation amplitude and initial phase difference to suppress chaos are determined.The chaotic motions can be successfully converted to some regular motions by weak periodic perturbations.The results of theoretical analyses are compared with numerical simulation,and they are in good agreement.This paper extends the research scope of nonlinear elastic dynamics,and provides a strategy for controlling chaotic responses of hyperelastic structures.
基金Project supported in part by the National Natural Science Foundation of China(Grant Nos.62005129 and 62175116)。
文摘We experimentally analyze the effect of the optical power on the time delay signature identification and the random bit generation in chaotic semiconductor laser with optical feedback.Due to the inevitable noise during the photoelectric detection and analog-digital conversion,the varying of output optical power would change the signal to noise ratio,then impact time delay signature identification and the random bit generation.Our results show that,when the optical power is less than-14 dBm,with the decreasing of the optical power,the actual identified time delay signature degrades and the entropy of the chaotic signal increases.Moreover,the extracted random bit sequence with lower optical power is more easily pass through the randomness testing.
基金Project supported by the National Natural Science Foundation of China(Grant No.12275165)XGW was also supported by the Fundamental Research Funds for the Central Universities(Grant No.GK202202003).
文摘Model-free,data-driven prediction of chaotic motions is a long-standing challenge in nonlinear science.Stimulated by the recent progress in machine learning,considerable attention has been given to the inference of chaos by the technique of reservoir computing(RC).In particular,by incorporating a parameter-control channel into the standard RC,it is demonstrated that the machine is able to not only replicate the dynamics of the training states,but also infer new dynamics not included in the training set.The new machine-learning scheme,termed parameter-aware RC,opens up new avenues for data-based analysis of chaotic systems,and holds promise for predicting and controlling many real-world complex systems.Here,using typical chaotic systems as examples,we give a comprehensive introduction to this powerful machine-learning technique,including the algorithm,the implementation,the performance,and the open questions calling for further studies.
基金supported by the special foundation for Guangxi Ba Gui Scholars and Junwu Scholars of Guangxi Universitysupported by the National Natural Science Foundation of China(Grant No.12475049)。
文摘Using the Melnikov method,the phenomenon of thermal chaos under periodic perturbation in the extended phase space of the modified thermodynamics of Kerr-AdS black holes is investigated.On the(P,v)section in the extended phase space,it is shown that temporal chaos will appear in the unstable spinodal region when the perturbation amplitude is larger than critical value δ_(c)^(Pv).We findδ_(c)^(Pv) is monotonically decreasing with respect to the angular momentum parameter a,which implies a large a leads to chaotic behavior more easily under time-periodic thermal perturbation.Similarly,on the(Ω_(H),J)section,we show there exists a critical value δ_(c)^(ΩJ) which depends on the cosmological parameter l=√-3/Λ.When the perturbation amplitude exceeds δ_(c)^(ΩJ),temporal chaos occurs.As l increases,chaos becomes easier.For spatial perturbation,chaos always exists irrespective of perturbation amplitude in both the(P,v)section and(Ω_(H),J)section.
基金supported by the National Natural Science Foundation of China under Grant Nos.12275078,11875026,12035005 and 2020YFC2201400Science Foundation of Hengyang Normal University of China under Contract No.2020QD24sponsored by the innovative research group of Hunan Province under Grant No.2024JJ1006。
文摘As one of the famous effects in the quantum Rabi model(QRM),Rabi oscillation may lead to the occurrence of quantum dynamical behaviors without classical dynamic counterparts,such as quantum collapse and revival effects.In this paper,we focus on studying the long-time quantum signatures of chaos in the large atom-light frequency ratios of the Rabi model.It is shown that the saturated values of the entanglement entropy for initial states located in chaotic sea are higher than that in the regular regions,and the Husimi Q function are more dispersed in phase space.Moreover,we observed that the long-time average entanglement entropy and spin variance correspond well with the semiclassical phase space.Our results imply that the correspondence principle is not invalidated by quantum collapse and revival effects in the large atom-light frequency ratios Rabi model.
基金support from the National Natural Science Foundation of China(Grant Nos.52174123&52274222).
文摘This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.
