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
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
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
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
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
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 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
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 dynamics of vapor−liquid−solid(V−L−S)flow boiling in fluidized bed evaporators exhibit inherent complexity and chaotic behavior,hindering accurate prediction of pressure drop signals.To address this challenge,this...The dynamics of vapor−liquid−solid(V−L−S)flow boiling in fluidized bed evaporators exhibit inherent complexity and chaotic behavior,hindering accurate prediction of pressure drop signals.To address this challenge,this study proposes an innovative hybrid approach that integrates wavelet neural network(WNN)with chaos analysis.By leveraging the Cross-Correlation(C−C)method,the minimum embedding dimension for phase space reconstruction is systematically calculated and then adopted as the input node configuration for the WNN.Simulation results demonstrate the remarkable effectiveness of this integrated method in predicting pressure drop signals,advancing our understanding of the intricate dynamic phenomena occurring with V−L−S fluidized bed evaporators.Moreover,this study offers a novel perspective on applying advanced data-driven techniques to handle the complexities of multi-phase flow systems and highlights the potential for improved operational prediction and control in industrial settings.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
As a crucial component of intelligent chassis systems,air suspension significantly enhances driver comfort and vehicle stability.To further improve the adaptability of commercial vehicles to complex and variable road ...As a crucial component of intelligent chassis systems,air suspension significantly enhances driver comfort and vehicle stability.To further improve the adaptability of commercial vehicles to complex and variable road conditions,this paper proposes a linear motor active suspension with quasi-zero stiffness(QZS)air spring system.Firstly,a dynamic model of the linear motor active suspension with QZS air spring system is established.Secondly,considering the random uncertainties in the linear motor parameters due to manufacturing and environmental factors,a dynamic model and state equations incorporating these uncertainties are constructed using the polynomial chaos expansion(PCE)method.Then,based on H_(2) robust control theory and the Kalman filter,a state feedback control law is derived,accounting for the random parameter uncertainties.Finally,simulation and hardware-in-the-loop(HIL)experimental results demonstrate that the PCE-H_(2) robust controller not only provides better performance in terms of vehicle ride comfort compared to general H_(2) robust controller but also exhibits higher robustness to the effects of random uncertain parameters,resulting in more stable control performance.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
Chaos synchronization of coupled nonlinear systems is ubiquitous in nature and science. Dynamic behaviors of coupled ring and linear arrays of unidirectionally coupled Lorenz oscillators are studied numerically. We fi...Chaos synchronization of coupled nonlinear systems is ubiquitous in nature and science. Dynamic behaviors of coupled ring and linear arrays of unidirectionally coupled Lorenz oscillators are studied numerically. We find that chaos synchronization in circular arrays of chaotic systems can occur through the on off intermittent synchronization with a power law distribution of laminar phases. And in the coupled ring and linear array it is found that the chaotic rotating waves generated from the ring propagate with spatial periodic synchronization along the linear array.展开更多
This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investi...This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. By numerical simulating, this paper verifies that the four-dimensional system can evolve into periodic, quasi-periodic, chaotic and hyperchaotic behaviours. And the new dynamical system is hyperchaotic in a large region. In comparison with other known hyperchaos, the two positive Lyapunov exponents of the new system are relatively more larger. Thus it has more complex degree.展开更多
In this paper, a non-existence condition for homoclinic and heteroclinic orbits in n-dimensional, continuous-time, and smooth systems is obtained, Based on this result and an elementary example, it can be conjectured ...In this paper, a non-existence condition for homoclinic and heteroclinic orbits in n-dimensional, continuous-time, and smooth systems is obtained, Based on this result and an elementary example, it can be conjectured that there is a fourth kind of chaos in polynomial ordinary differential equation （ODE） systems characterized by the nonexistence of homoclinic and heteroclinic orbits.展开更多
A paper, ＂Non-existence of Shilnikov chaos in continuous-time systems＂ was published in the journal Applied Mathematics and Mechanics （English Edition）. The authors gave sufficient conditions for the non-existence...A paper, ＂Non-existence of Shilnikov chaos in continuous-time systems＂ was published in the journal Applied Mathematics and Mechanics （English Edition）. The authors gave sufficient conditions for the non-existence of homoclinic and heteroclinic orbits in an nth-order autonomous system. Unfortunately, we show in this comment that the proof presented is erroneous and the result is invalid. We also provide two counterexamples of the wrong criterion stated by the authors.展开更多
This paper presents a low power,truly random number generator （TRNG） based on a simple chaotic map of the Bernoulli shift,which is extended to remain robustness in implementation. The map is realized by switched-cur...This paper presents a low power,truly random number generator （TRNG） based on a simple chaotic map of the Bernoulli shift,which is extended to remain robustness in implementation. The map is realized by switched-current techniques that can fully integrate it in a cryptosystem on a chip. A pipelined architecture post-processed by a simple XOR circuit is used to improve the entropy. The TRNG is fabricated in an HJTC 0.18μm CMOS mixed signal process,and the statistical properties are investigated by measurement results. The power consumption is only 1.42mW and the truly random output bit rate is 10Mbit/s.展开更多
In order to realize the coordination oriented management of the economy resource environment(Ec R Ev) composite system,its optimal aggregate coordinating measurement model is established.A self learning method is...In order to realize the coordination oriented management of the economy resource environment(Ec R Ev) composite system,its optimal aggregate coordinating measurement model is established.A self learning method is presented,which combines the optimizing technology and stability analysis together to achieve a tradeoff between the optimizing objective and system stability.So a model for chaos control of the composite system based on coordination is proposed.展开更多
As one of secure communication means, chaotic communication systems has been well-developed during the past three decades. Technical papers, both for theoretical and practical investigations, have reached a huge amoun...As one of secure communication means, chaotic communication systems has been well-developed during the past three decades. Technical papers, both for theoretical and practical investigations, have reached a huge amount in number. On the other hand, fractional chaos, as a parallel ongoing research topic, also attracts many researchers to investigate. As far as the IT field is concerned, the research on control systems by using fractional chaos known as FOC （fractional order control） has been a hot issue for quite a long time. As a comparison, interesting enough, up to now we have not found any research result related to Fractional Chaos Communi- cation （FCC） system, i.e., a system based on fractional chaos. The motivation of the present article is to reveal the feasibility of realizing communication systems based upon FCC and their superiority over the conventional integer chaotic communication systems. Principles of FCC and its advantages over integer chaotic communication systems are also discussed.展开更多
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.
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.
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.
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supported by the open foundation of State Key Laboratory of Chemical Engineering(SKL-ChE-22B01)the Natural Science Foundation of China(22008169).
文摘The dynamics of vapor−liquid−solid(V−L−S)flow boiling in fluidized bed evaporators exhibit inherent complexity and chaotic behavior,hindering accurate prediction of pressure drop signals.To address this challenge,this study proposes an innovative hybrid approach that integrates wavelet neural network(WNN)with chaos analysis.By leveraging the Cross-Correlation(C−C)method,the minimum embedding dimension for phase space reconstruction is systematically calculated and then adopted as the input node configuration for the WNN.Simulation results demonstrate the remarkable effectiveness of this integrated method in predicting pressure drop signals,advancing our understanding of the intricate dynamic phenomena occurring with V−L−S fluidized bed evaporators.Moreover,this study offers a novel perspective on applying advanced data-driven techniques to handle the complexities of multi-phase flow systems and highlights the potential for improved operational prediction and control in industrial settings.
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Supported by National Natural Science Foundation of China(Grant No.51875256)Open Platform Fund of Human Institute of Technology(Grant No.KFA22009).
文摘As a crucial component of intelligent chassis systems,air suspension significantly enhances driver comfort and vehicle stability.To further improve the adaptability of commercial vehicles to complex and variable road conditions,this paper proposes a linear motor active suspension with quasi-zero stiffness(QZS)air spring system.Firstly,a dynamic model of the linear motor active suspension with QZS air spring system is established.Secondly,considering the random uncertainties in the linear motor parameters due to manufacturing and environmental factors,a dynamic model and state equations incorporating these uncertainties are constructed using the polynomial chaos expansion(PCE)method.Then,based on H_(2) robust control theory and the Kalman filter,a state feedback control law is derived,accounting for the random parameter uncertainties.Finally,simulation and hardware-in-the-loop(HIL)experimental results demonstrate that the PCE-H_(2) robust controller not only provides better performance in terms of vehicle ride comfort compared to general H_(2) robust controller but also exhibits higher robustness to the effects of random uncertain parameters,resulting in more stable control performance.
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.
文摘Chaos synchronization of coupled nonlinear systems is ubiquitous in nature and science. Dynamic behaviors of coupled ring and linear arrays of unidirectionally coupled Lorenz oscillators are studied numerically. We find that chaos synchronization in circular arrays of chaotic systems can occur through the on off intermittent synchronization with a power law distribution of laminar phases. And in the coupled ring and linear array it is found that the chaotic rotating waves generated from the ring propagate with spatial periodic synchronization along the linear array.
基金Project supported by the National Nature Science Foundation of China （Grant No 60574036）, the Specialized Research Fund for the Doctoral Program of China （Grant No 20050055013） and the Program for New Excellent Talents in University of China （NCET）.
文摘This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. By numerical simulating, this paper verifies that the four-dimensional system can evolve into periodic, quasi-periodic, chaotic and hyperchaotic behaviours. And the new dynamical system is hyperchaotic in a large region. In comparison with other known hyperchaos, the two positive Lyapunov exponents of the new system are relatively more larger. Thus it has more complex degree.
文摘In this paper, a non-existence condition for homoclinic and heteroclinic orbits in n-dimensional, continuous-time, and smooth systems is obtained, Based on this result and an elementary example, it can be conjectured that there is a fourth kind of chaos in polynomial ordinary differential equation （ODE） systems characterized by the nonexistence of homoclinic and heteroclinic orbits.
基金supported by the Ministerio de Educacion y Ciencia,Plan Nacional I+D+I co-financed with FEDER Funds(No.MTM2010-20907-C02)the Consejeria de Educacion y Ciencia de la Juntade Andalucia(Nos.FQM-276,TIC-0130,and P08-FQM-03770)
文摘A paper, ＂Non-existence of Shilnikov chaos in continuous-time systems＂ was published in the journal Applied Mathematics and Mechanics （English Edition）. The authors gave sufficient conditions for the non-existence of homoclinic and heteroclinic orbits in an nth-order autonomous system. Unfortunately, we show in this comment that the proof presented is erroneous and the result is invalid. We also provide two counterexamples of the wrong criterion stated by the authors.
文摘This paper presents a low power,truly random number generator （TRNG） based on a simple chaotic map of the Bernoulli shift,which is extended to remain robustness in implementation. The map is realized by switched-current techniques that can fully integrate it in a cryptosystem on a chip. A pipelined architecture post-processed by a simple XOR circuit is used to improve the entropy. The TRNG is fabricated in an HJTC 0.18μm CMOS mixed signal process,and the statistical properties are investigated by measurement results. The power consumption is only 1.42mW and the truly random output bit rate is 10Mbit/s.
基金Supported by National Natural Science Foundation of China(No.79970 0 4 3)
文摘In order to realize the coordination oriented management of the economy resource environment(Ec R Ev) composite system,its optimal aggregate coordinating measurement model is established.A self learning method is presented,which combines the optimizing technology and stability analysis together to achieve a tradeoff between the optimizing objective and system stability.So a model for chaos control of the composite system based on coordination is proposed.
文摘As one of secure communication means, chaotic communication systems has been well-developed during the past three decades. Technical papers, both for theoretical and practical investigations, have reached a huge amount in number. On the other hand, fractional chaos, as a parallel ongoing research topic, also attracts many researchers to investigate. As far as the IT field is concerned, the research on control systems by using fractional chaos known as FOC （fractional order control） has been a hot issue for quite a long time. As a comparison, interesting enough, up to now we have not found any research result related to Fractional Chaos Communi- cation （FCC） system, i.e., a system based on fractional chaos. The motivation of the present article is to reveal the feasibility of realizing communication systems based upon FCC and their superiority over the conventional integer chaotic communication systems. Principles of FCC and its advantages over integer chaotic communication systems are also discussed.
