Ensuring information security in the quantum era is a growing challenge due to advancements in cryptographic attacks and the emergence of quantum computing.To address these concerns,this paper presents the mathematica...Ensuring information security in the quantum era is a growing challenge due to advancements in cryptographic attacks and the emergence of quantum computing.To address these concerns,this paper presents the mathematical and computer modeling of a novel two-dimensional(2D)chaotic system for secure key generation in quantum image encryption(QIE).The proposed map employs trigonometric perturbations in conjunction with rational-saturation functions and hence,named as Trigonometric-Rational-Saturation(TRS)map.Through rigorous mathematical analysis and computational simulations,the map is extensively evaluated for bifurcation behaviour,chaotic trajectories,and Lyapunov exponents.The security evaluation validates the map’s non-linearity,unpredictability,and sensitive dependence on initial conditions.In addition,the proposed TRS map has further been tested by integrating it in a QIE scheme.The QIE scheme first quantum-encodes the classic image using the Novel Enhanced Quantum Representation(NEQR)technique,the TRS map is used for the generation of secure diffusion key,which is XOR-ed with the quantum-ready image to obtain the encrypted images.The security evaluation of the QIE scheme demonstrates superior security of the encrypted images in terms of statistical security attacks and also against Differential attacks.The encrypted images exhibit zero correlation and maximum entropy with demonstrating strong resilience due to 99.62%and 33.47%results for Number of Pixels Change Rate(NPCR)and Unified Average Changing Intensity(UACI).The results validate the effectiveness of TRS-based quantum encryption scheme in securing digital images against emerging quantum threats,making it suitable for secure image encryption in IoT and edge-based applications.展开更多
Ensuring the integrity and confidentiality of patient medical information is a critical priority in the healthcare sector.In the context of security,this paper proposes a novel encryption algorithm that integrates Blo...Ensuring the integrity and confidentiality of patient medical information is a critical priority in the healthcare sector.In the context of security,this paper proposes a novel encryption algorithm that integrates Blockchain technology,aiming to improve the security and privacy of transmitted data.The proposed encryption algorithm is a block-cipher image encryption scheme based on different chaotic maps:The logistic Map,the Tent Map,and the Henon Map used to generate three encryption keys.The proposed block-cipher system employs the Hilbert curve to perform permutation while a generated chaos-based S-Box is used to perform substitution.Furthermore,the integration of a Blockchain-based solution for securing data transmission and communication between nodes and authenticating the encrypted medical image’s authenticity adds a layer of security to our proposed method.Our proposed cryptosystem is divided into two principal modules presented as a pseudo-random number generator(PRNG)used for key generation and an encryption and decryption system based on the properties of confusion and diffusion.The security analysis and experimental tests for the proposed algorithm show that the average value of the information entropy of the encrypted images is 7.9993,the Number of Pixels Change Rate(NPCR)values are over 99.5%and the Unified Average Changing Intensity(UACI)values are greater than 33%.These results prove the strength of our proposed approach,demonstrating that it can significantly enhance the security of encrypted images.展开更多
One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite...One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite equilibria exhibits complex bifurcation characteris-tics.The Hopf bifurcation and hidden attractors with symmetric coexistence of the system are analyzed.An improved dynamic state feed-back control method is adopted to reduce the tedious calculation process to prevent the Hopf bifurcation from being controlled.A hybrid controller that includes both nonlinear and linear controllers is set up for the system.With the method,the delay and stability of the Hopf bifurcation of the system are studied and the goal of anti-control is achieved.Numerical analysis verified the correctness.展开更多
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 dynamics of chaotic memristor-based systems offer promising potential for secure communication.However,existing solutions frequently suffer from drawbacks such as slow synchronization,low key diversity,and poor no...The dynamics of chaotic memristor-based systems offer promising potential for secure communication.However,existing solutions frequently suffer from drawbacks such as slow synchronization,low key diversity,and poor noise resistance.To overcome these issues,a novel fractional-order chaotic system incorporating a memristor emulator derived from the Shinriki oscillator is proposed.The main contribution lies in the enhanced dynamic complexity and flexibility of the proposed architecture,making it suitable for cryptographic applications.Furthermore,the feasibility of synchronization to ensure secure data transmission is demonstrated through the validation of two strategies:an active control method ensuring asymptotic convergence,and a finite-time control method enabling faster stabilization.The robustness of the scheme is confirmed by simulation results on a color image:χ^(2)=253/237/267(R/G/B);entropy≈7.993;correlations between adjacent pixels in all directions are close to zero(e.g.,-0.0318 vertically);and high number of pixel change rate and unified average changing intensity(e.g.,33.40%and 99.61%,respectively).Peak signal-to-noise ratio analysis shows that resilience to noise and external disturbances is maintained.It is shown that multiple fractional orders further enrich the chaotic behavior,increasing the systems suitability for secure communication in embedded environments.These findings highlight the relevance of fractional-order chaotic memristive systems for lightweight secure transmission applications.展开更多
This study examines the spatiotemporal evolution of Tibetan villages in western Sichuan through state transition models and predictive simulations to understand their complex dynamics and key driving factors.Using a c...This study examines the spatiotemporal evolution of Tibetan villages in western Sichuan through state transition models and predictive simulations to understand their complex dynamics and key driving factors.Using a combination of multivariate time-series analysis and chaotic attractor identification,the research identifies forest cover,economic growth,employment rates,road density,and communication network coverage as critical determinants of village trajectories.For instance,Molo Village recovers rapidly with a 10%increase in regional economic growth,while Xisuo Village becomes unstable with employment rate fluctuations above 2%.Shenzuo Village benefits from improved road density,and Minzu Village’s stability depends on forest cover.Jiangba Village relies on the growth of irrigated farmland and communication network coverage,whereas Kegeyi Village exhibits periodic dynamics and high sensitivity to employment variations.The findings underscore the inherent complexity and nonlinearity of rural systems,revealed through chaotic attractor analysis,which highlights the system’s sensitivity to initial conditions and external shocks.The article provides actionable insights into resilience mechanisms and offers practical recommendations for the sustainable development of culturally and ecologically sensitive regions.Emphasis on tailored management strategies is essential to meet the challenges faced by these unique systems in the face of modernization and environmental change.展开更多
Detecting the complexity of natural systems,such as hydrological systems,can help improve our understanding of complex interactions and feedback between variables in these systems.The correlation dimension method,as o...Detecting the complexity of natural systems,such as hydrological systems,can help improve our understanding of complex interactions and feedback between variables in these systems.The correlation dimension method,as one of the most useful methods,has been applied in many studies to investigate the chaos and detect the intrinsic dimensions of underlying dynamic systems.However,this method often relies on manual inspection due to uncertainties from iden-tifying the scaling region,making the correlation dimension value calculation troublesome and subjective.Therefore,it is necessary to propose a fast and intelligent algorithm to solve the above problem.This study implies the distinct windows tracking technique and fuzzy C-means clustering algorithm to accu-rately identify the scaling range and estimate the correlation dimension values.The proposed method is verified using the classic Lorenz chaotic system and 10 streamflow series in the Daling River basin of Liaoning Province,China.The results reveal that the proposed method is an intelligent and robust method for rapidly and accurately calculating the correlation dimension values,and the average operation efficiency of the proposed algorithm is 30 times faster than that of the original Grassberger-Procaccia algorithm.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
The principle of optical time-domain reflection localization limits the sensing spatial resolution of Raman distributed optical fiber sensing.We provide a solution for a Raman distributed optical fiber sensing system ...The principle of optical time-domain reflection localization limits the sensing spatial resolution of Raman distributed optical fiber sensing.We provide a solution for a Raman distributed optical fiber sensing system with kilometer-level sensing distance and submeter spatial resolution.Based on this,we propose a Raman distributed optical fiber sensing scheme based on chaotic pulse cluster demodulation.Chaotic pulse clusters are used as the probe signal,in preference to conventional pulsed or chaotic single-pulse lasers.Furthermore,the accurate positioning of the temperature variety region along the sensing fiber can be realized using chaotic pulse clusters.The proposed demodulation scheme can enhance the signal-to-noise ratio by improving the correlation between the chaotic reference and the chaotic Raman anti-Stokes scattering signals.The experiment achieved a sensing spatial resolution of 30 cm at a distributed temperature-sensing distance of∼6.0 km.Furthermore,we explored the influence of chaotic pulse width and detector bandwidth on the sensing spatial resolution.In addition,the theoretical experiments proved that the sensing spatial resolution in the proposed scheme was independent of the pulse width and sensing distance.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
Duality analysis of time series and complex networks has been a frontier topic during the last several decades.According to some recent approaches in this direction,the intrinsic dynamics of typical nonlinear systems ...Duality analysis of time series and complex networks has been a frontier topic during the last several decades.According to some recent approaches in this direction,the intrinsic dynamics of typical nonlinear systems can be better characterized by considering the related nonlinear time series from the perspective of networks science.In this paper,the associated network family of the unified piecewise-linear(PWL)chaotic family,which can bridge the gap of the PWL chaotic Lorenz system and the PWL chaotic Chen system,was firstly constructed and analyzed.We constructed the associated network family via the original and the modified frequency-degree mapping strategy,as well as the classical visibility graph and horizontal visibility graph strategy,after removing the transient states.Typical related network characteristics,including the network fractal dimension,of the associated network family,are computed with changes of single key parameter a.These characteristic vectors of the network are also compared with the largest Lyapunov exponent(LLE)vector of the related original dynamical system.It can be found that,some network characteristics are highly correlated with LLE vector of the original nonlinear system,i.e.,there is an internal consistency between the largest Lyapunov exponents,some typical associated network characteristics,and the related network fractal dimension index.Numerical results show that the modified frequency-degree mapping strategy can demonstrate highest correlation,which means it can behave better to capture the intrinsic characteristics of the unified PWL chaotic family.展开更多
This paper proposes a universal impulse-function-based method for extending discrete chaotic maps,enabling flexible construction of multicavity chaotic attractors.The proposed method achieves one-directional(1D)/two-d...This paper proposes a universal impulse-function-based method for extending discrete chaotic maps,enabling flexible construction of multicavity chaotic attractors.The proposed method achieves one-directional(1D)/two-directional(2D)extensions without introducing additional nonlinear terms or altering system stability.Theoretically,the cavity quantity in arbitrary directions is controlled by adjusting impulse levels N,while the amplitude regulation is implemented through modifications to the proportionality parameter r.Theoretical analyses,including Lyapunov exponents(LEs)and bifurcation diagrams,are conducted,confirming that the extended maps retain the intrinsic dynamics of five rational map classes.The field-programmable gate array(FPGA)implementation results are consistent with the numerical simulation results,verifying the correctness of the theoretical analysis.The method enables the expansion of unipolar attractors and enhances entropy metrics,offering a robust framework for applications in secure communication,encryption,and chaos-based technologies.展开更多
Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urge...Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urgency of demand at disaster-affected sites. Firstly, urgency cost, economic cost, and transportation distance cost were identified as key objectives. The study applied fuzzy theory integration to construct a triangular fuzzy multi-objective site selection decision model. Next, the defuzzification theory transformed the fuzzy decision model into a precise one. Subsequently, an improved Chaotic Quantum Multi-Objective Harris Hawks Optimization (CQ-MOHHO) algorithm was proposed to solve the model. The CQ-MOHHO algorithm was shown to rapidly produce high-quality Pareto front solutions and identify optimal site selection schemes for emergency resource distribution centers through case studies. This outcome verified the feasibility and efficacy of the site selection decision model and the CQ-MOHHO algorithm. To further assess CQ-MOHHO’s performance, Zitzler-Deb-Thiele (ZDT) test functions, commonly used in multi-objective optimization, were employed. Comparisons with Multi-Objective Harris Hawks Optimization (MOHHO), Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Multi-Objective Grey Wolf Optimizer (MOGWO) using Generational Distance (GD), Hypervolume (HV), and Inverted Generational Distance (IGD) metrics showed that CQ-MOHHO achieved superior global search ability, faster convergence, and higher solution quality. The CQ-MOHHO algorithm efficiently achieved a balance between multiple objectives, providing decision-makers with satisfactory solutions and a valuable reference for researching and applying emergency site selection problems.展开更多
This paper introduces a novel chattering-free terminal sliding mode control(SMC)strategy to address chaotic behavior in permanent magnet synchronous generators(PMSG)for offshore wind turbine systems.By integrating an ...This paper introduces a novel chattering-free terminal sliding mode control(SMC)strategy to address chaotic behavior in permanent magnet synchronous generators(PMSG)for offshore wind turbine systems.By integrating an adaptive exponential reaching law with a continuous barrier function,the proposed approach eliminates chattering and ensures robust performance under model uncertainties.The methodology combines adaptive SMC with dynamic switching to estimate and compensates for unknown uncertainties,providing smooth and stable control.Finally,the performance and effectiveness of the proposed approach are compared with those of a previous study.展开更多
Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Nume...Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Numerical approaches have become necessary and sufficient to be addressed and employed for benefiting from the adaptability of such systems for varied applications.A variety of fractional Layla and Majnun model(LMM)system kinds has been proposed in the current work where some of these systems’key behaviors are addressed.In addition,the necessary and sufficient conditions for the stability and asymptotic stability of the fractional dynamic systems are investigated,as a result of which,the necessary requirements of the LMM to achieve constant and asymptotically steady zero resolutions are provided.As a special case,when Layla and Majnun have equal feelings,we propose an analysis of the system in view of its equilibrium and fixed point sets.Considering that the system has marginal stability if its eigenvalues have both negative and zero real portions,it is demonstrated that the system neither converges nor diverges to a steady trajectory or equilibrium point.It,rather,continues to hover along the line separating stability and instability based on the fractional LMM system.展开更多
This paper presents both analytical and numerical studies of the conservative Sawada-Kotera equation and its dissipative generalization,equations known for their soliton solutions and rich chaotic dynamics.These model...This paper presents both analytical and numerical studies of the conservative Sawada-Kotera equation and its dissipative generalization,equations known for their soliton solutions and rich chaotic dynamics.These models offer valuable insights into nonlinear wave propagation,with applications in fluid dynamics and materials science,including systems such as liquid crystals and ferrofluids.It is shown that the conservative Sawada-Kotera equation supports traveling wave solutions corresponding to elliptic limit cycles,as well as two-and three-dimensional invariant tori surrounding these cycles in the associated ordinary differential equation(ODE)system.For the dissipative generalized Sawada-Kotera equation,chaotic wave behavior is observed.The transition to chaos in the corresponding ODE systemfollows a universal bifurcation scenario consistent with the framework established by FShM(Feigenbaum-Sharkovsky-Magnitskii)theory.Notably,this study demonstrates for the first time that the conservative Sawada-Kotera equation can exhibit complex quasi-periodic wave solutions,while its dissipative counterpart admits an infinite number of stable periodic and chaotic waveforms.展开更多
The methods to determine time delays and embedding dimensions in the phase space delay reconstruction of multivariate chaotic time series are proposed. Three nonlinear prediction methods of multivariate chaotic tim...The methods to determine time delays and embedding dimensions in the phase space delay reconstruction of multivariate chaotic time series are proposed. Three nonlinear prediction methods of multivariate chaotic time series including local mean prediction, local linear prediction and BP neural networks prediction are considered. The simulation results obtained by the Lorenz system show that no matter what nonlinear prediction method is used, the prediction error of multivariate chaotic time series is much smaller than the prediction error of univariate time series, even if half of the data of univariate time series are used in multivariate time series. The results also verify that methods to determine the time delays and the embedding dimensions are correct from the view of minimizing the prediction error.展开更多
The chaotic dynamic behaviors of a reduction of perturbed Korteweg-de Vries （KdV） equation in form of a parametric excitation are studied. Chaotic behaviors from homoclinic crossings are analyzed with an improved Me...The chaotic dynamic behaviors of a reduction of perturbed Korteweg-de Vries （KdV） equation in form of a parametric excitation are studied. Chaotic behaviors from homoclinic crossings are analyzed with an improved Melnikov method and are compared for the systems with a periodically external excitation, with a linear periodically parametric excitation, or with a nonlinear periodically excitation. The critical curves separating chaotic regions and non-chaotic regions of the above systems are different from each other. Especially, a dead frequency is presented for the system with a nonlinear periodically parametric excitation. The chaos excited at the frequency does not occur no matter how large the excitation amplitude is. A time integration scheme is used to find the numerical solutions of these systems. Numerical results agree with the analytical ones.展开更多
基金funded by Deanship of Research and Graduate Studies at King Khalid University.The authors extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Group Project under grant number(RGP.2/556/45).
文摘Ensuring information security in the quantum era is a growing challenge due to advancements in cryptographic attacks and the emergence of quantum computing.To address these concerns,this paper presents the mathematical and computer modeling of a novel two-dimensional(2D)chaotic system for secure key generation in quantum image encryption(QIE).The proposed map employs trigonometric perturbations in conjunction with rational-saturation functions and hence,named as Trigonometric-Rational-Saturation(TRS)map.Through rigorous mathematical analysis and computational simulations,the map is extensively evaluated for bifurcation behaviour,chaotic trajectories,and Lyapunov exponents.The security evaluation validates the map’s non-linearity,unpredictability,and sensitive dependence on initial conditions.In addition,the proposed TRS map has further been tested by integrating it in a QIE scheme.The QIE scheme first quantum-encodes the classic image using the Novel Enhanced Quantum Representation(NEQR)technique,the TRS map is used for the generation of secure diffusion key,which is XOR-ed with the quantum-ready image to obtain the encrypted images.The security evaluation of the QIE scheme demonstrates superior security of the encrypted images in terms of statistical security attacks and also against Differential attacks.The encrypted images exhibit zero correlation and maximum entropy with demonstrating strong resilience due to 99.62%and 33.47%results for Number of Pixels Change Rate(NPCR)and Unified Average Changing Intensity(UACI).The results validate the effectiveness of TRS-based quantum encryption scheme in securing digital images against emerging quantum threats,making it suitable for secure image encryption in IoT and edge-based applications.
基金supported by the Large Group Project under grant number(RGP2/473/46).
文摘Ensuring the integrity and confidentiality of patient medical information is a critical priority in the healthcare sector.In the context of security,this paper proposes a novel encryption algorithm that integrates Blockchain technology,aiming to improve the security and privacy of transmitted data.The proposed encryption algorithm is a block-cipher image encryption scheme based on different chaotic maps:The logistic Map,the Tent Map,and the Henon Map used to generate three encryption keys.The proposed block-cipher system employs the Hilbert curve to perform permutation while a generated chaos-based S-Box is used to perform substitution.Furthermore,the integration of a Blockchain-based solution for securing data transmission and communication between nodes and authenticating the encrypted medical image’s authenticity adds a layer of security to our proposed method.Our proposed cryptosystem is divided into two principal modules presented as a pseudo-random number generator(PRNG)used for key generation and an encryption and decryption system based on the properties of confusion and diffusion.The security analysis and experimental tests for the proposed algorithm show that the average value of the information entropy of the encrypted images is 7.9993,the Number of Pixels Change Rate(NPCR)values are over 99.5%and the Unified Average Changing Intensity(UACI)values are greater than 33%.These results prove the strength of our proposed approach,demonstrating that it can significantly enhance the security of encrypted images.
基金Supported by the Guiding Project of Science and Technology Research Plan of Hubei Provincial Department of Education(B2022458)。
文摘One method to change the bifurcation characteristics of chaotic systems is anti-control,which can either delay or advance bifur-cation and transform an unstable state into a stable one.The chaotic system with infinite equilibria exhibits complex bifurcation characteris-tics.The Hopf bifurcation and hidden attractors with symmetric coexistence of the system are analyzed.An improved dynamic state feed-back control method is adopted to reduce the tedious calculation process to prevent the Hopf bifurcation from being controlled.A hybrid controller that includes both nonlinear and linear controllers is set up for the system.With the method,the delay and stability of the Hopf bifurcation of the system are studied and the goal of anti-control is achieved.Numerical analysis verified the correctness.
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.
文摘The dynamics of chaotic memristor-based systems offer promising potential for secure communication.However,existing solutions frequently suffer from drawbacks such as slow synchronization,low key diversity,and poor noise resistance.To overcome these issues,a novel fractional-order chaotic system incorporating a memristor emulator derived from the Shinriki oscillator is proposed.The main contribution lies in the enhanced dynamic complexity and flexibility of the proposed architecture,making it suitable for cryptographic applications.Furthermore,the feasibility of synchronization to ensure secure data transmission is demonstrated through the validation of two strategies:an active control method ensuring asymptotic convergence,and a finite-time control method enabling faster stabilization.The robustness of the scheme is confirmed by simulation results on a color image:χ^(2)=253/237/267(R/G/B);entropy≈7.993;correlations between adjacent pixels in all directions are close to zero(e.g.,-0.0318 vertically);and high number of pixel change rate and unified average changing intensity(e.g.,33.40%and 99.61%,respectively).Peak signal-to-noise ratio analysis shows that resilience to noise and external disturbances is maintained.It is shown that multiple fractional orders further enrich the chaotic behavior,increasing the systems suitability for secure communication in embedded environments.These findings highlight the relevance of fractional-order chaotic memristive systems for lightweight secure transmission applications.
文摘This study examines the spatiotemporal evolution of Tibetan villages in western Sichuan through state transition models and predictive simulations to understand their complex dynamics and key driving factors.Using a combination of multivariate time-series analysis and chaotic attractor identification,the research identifies forest cover,economic growth,employment rates,road density,and communication network coverage as critical determinants of village trajectories.For instance,Molo Village recovers rapidly with a 10%increase in regional economic growth,while Xisuo Village becomes unstable with employment rate fluctuations above 2%.Shenzuo Village benefits from improved road density,and Minzu Village’s stability depends on forest cover.Jiangba Village relies on the growth of irrigated farmland and communication network coverage,whereas Kegeyi Village exhibits periodic dynamics and high sensitivity to employment variations.The findings underscore the inherent complexity and nonlinearity of rural systems,revealed through chaotic attractor analysis,which highlights the system’s sensitivity to initial conditions and external shocks.The article provides actionable insights into resilience mechanisms and offers practical recommendations for the sustainable development of culturally and ecologically sensitive regions.Emphasis on tailored management strategies is essential to meet the challenges faced by these unique systems in the face of modernization and environmental change.
基金IWHR Basic Scientific Research Project,Grant/Award Number:JZ110145B0072024IWHR Internationally-Oriented Talent for International Academic Leader Program,Grant/Award Number:0203982012National Natural Science Foundation of China,Grant/Award Number:51609257。
文摘Detecting the complexity of natural systems,such as hydrological systems,can help improve our understanding of complex interactions and feedback between variables in these systems.The correlation dimension method,as one of the most useful methods,has been applied in many studies to investigate the chaos and detect the intrinsic dimensions of underlying dynamic systems.However,this method often relies on manual inspection due to uncertainties from iden-tifying the scaling region,making the correlation dimension value calculation troublesome and subjective.Therefore,it is necessary to propose a fast and intelligent algorithm to solve the above problem.This study implies the distinct windows tracking technique and fuzzy C-means clustering algorithm to accu-rately identify the scaling range and estimate the correlation dimension values.The proposed method is verified using the classic Lorenz chaotic system and 10 streamflow series in the Daling River basin of Liaoning Province,China.The results reveal that the proposed method is an intelligent and robust method for rapidly and accurately calculating the correlation dimension values,and the average operation efficiency of the proposed algorithm is 30 times faster than that of the original Grassberger-Procaccia algorithm.
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.
基金supported by the National Natural Science Foundation of China(Grant Nos.U23A20375 and 62075151)the National Key Research and Development Program of China(Grant No.202103021223042).
文摘The principle of optical time-domain reflection localization limits the sensing spatial resolution of Raman distributed optical fiber sensing.We provide a solution for a Raman distributed optical fiber sensing system with kilometer-level sensing distance and submeter spatial resolution.Based on this,we propose a Raman distributed optical fiber sensing scheme based on chaotic pulse cluster demodulation.Chaotic pulse clusters are used as the probe signal,in preference to conventional pulsed or chaotic single-pulse lasers.Furthermore,the accurate positioning of the temperature variety region along the sensing fiber can be realized using chaotic pulse clusters.The proposed demodulation scheme can enhance the signal-to-noise ratio by improving the correlation between the chaotic reference and the chaotic Raman anti-Stokes scattering signals.The experiment achieved a sensing spatial resolution of 30 cm at a distributed temperature-sensing distance of∼6.0 km.Furthermore,we explored the influence of chaotic pulse width and detector bandwidth on the sensing spatial resolution.In addition,the theoretical experiments proved that the sensing spatial resolution in the proposed scheme was independent of the pulse width and sensing distance.
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.
文摘Duality analysis of time series and complex networks has been a frontier topic during the last several decades.According to some recent approaches in this direction,the intrinsic dynamics of typical nonlinear systems can be better characterized by considering the related nonlinear time series from the perspective of networks science.In this paper,the associated network family of the unified piecewise-linear(PWL)chaotic family,which can bridge the gap of the PWL chaotic Lorenz system and the PWL chaotic Chen system,was firstly constructed and analyzed.We constructed the associated network family via the original and the modified frequency-degree mapping strategy,as well as the classical visibility graph and horizontal visibility graph strategy,after removing the transient states.Typical related network characteristics,including the network fractal dimension,of the associated network family,are computed with changes of single key parameter a.These characteristic vectors of the network are also compared with the largest Lyapunov exponent(LLE)vector of the related original dynamical system.It can be found that,some network characteristics are highly correlated with LLE vector of the original nonlinear system,i.e.,there is an internal consistency between the largest Lyapunov exponents,some typical associated network characteristics,and the related network fractal dimension index.Numerical results show that the modified frequency-degree mapping strategy can demonstrate highest correlation,which means it can behave better to capture the intrinsic characteristics of the unified PWL chaotic family.
基金supported by the National Natural Science Foundation of China(Grant No.62001391)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2024A1515010308)+1 种基金the Natural Science Basic Research Program of Shaanxi(Grant No.2024JC-YBQN-0464)the Scientific Research Program Funded by Education Department of Shaanxi Provincial Government(Grant No.24JK0559).
文摘This paper proposes a universal impulse-function-based method for extending discrete chaotic maps,enabling flexible construction of multicavity chaotic attractors.The proposed method achieves one-directional(1D)/two-directional(2D)extensions without introducing additional nonlinear terms or altering system stability.Theoretically,the cavity quantity in arbitrary directions is controlled by adjusting impulse levels N,while the amplitude regulation is implemented through modifications to the proportionality parameter r.Theoretical analyses,including Lyapunov exponents(LEs)and bifurcation diagrams,are conducted,confirming that the extended maps retain the intrinsic dynamics of five rational map classes.The field-programmable gate array(FPGA)implementation results are consistent with the numerical simulation results,verifying the correctness of the theoretical analysis.The method enables the expansion of unipolar attractors and enhances entropy metrics,offering a robust framework for applications in secure communication,encryption,and chaos-based technologies.
文摘Addressing the complex issue of emergency resource distribution center site selection in uncertain environments, this study was conducted to comprehensively consider factors such as uncertainty parameters and the urgency of demand at disaster-affected sites. Firstly, urgency cost, economic cost, and transportation distance cost were identified as key objectives. The study applied fuzzy theory integration to construct a triangular fuzzy multi-objective site selection decision model. Next, the defuzzification theory transformed the fuzzy decision model into a precise one. Subsequently, an improved Chaotic Quantum Multi-Objective Harris Hawks Optimization (CQ-MOHHO) algorithm was proposed to solve the model. The CQ-MOHHO algorithm was shown to rapidly produce high-quality Pareto front solutions and identify optimal site selection schemes for emergency resource distribution centers through case studies. This outcome verified the feasibility and efficacy of the site selection decision model and the CQ-MOHHO algorithm. To further assess CQ-MOHHO’s performance, Zitzler-Deb-Thiele (ZDT) test functions, commonly used in multi-objective optimization, were employed. Comparisons with Multi-Objective Harris Hawks Optimization (MOHHO), Non-dominated Sorting Genetic Algorithm II (NSGA-II), and Multi-Objective Grey Wolf Optimizer (MOGWO) using Generational Distance (GD), Hypervolume (HV), and Inverted Generational Distance (IGD) metrics showed that CQ-MOHHO achieved superior global search ability, faster convergence, and higher solution quality. The CQ-MOHHO algorithm efficiently achieved a balance between multiple objectives, providing decision-makers with satisfactory solutions and a valuable reference for researching and applying emergency site selection problems.
文摘This paper introduces a novel chattering-free terminal sliding mode control(SMC)strategy to address chaotic behavior in permanent magnet synchronous generators(PMSG)for offshore wind turbine systems.By integrating an adaptive exponential reaching law with a continuous barrier function,the proposed approach eliminates chattering and ensures robust performance under model uncertainties.The methodology combines adaptive SMC with dynamic switching to estimate and compensates for unknown uncertainties,providing smooth and stable control.Finally,the performance and effectiveness of the proposed approach are compared with those of a previous study.
基金supported by Ajman University Internal Research Grant No.(DRGS Ref.2024-IRGHBS-3).
文摘Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Numerical approaches have become necessary and sufficient to be addressed and employed for benefiting from the adaptability of such systems for varied applications.A variety of fractional Layla and Majnun model(LMM)system kinds has been proposed in the current work where some of these systems’key behaviors are addressed.In addition,the necessary and sufficient conditions for the stability and asymptotic stability of the fractional dynamic systems are investigated,as a result of which,the necessary requirements of the LMM to achieve constant and asymptotically steady zero resolutions are provided.As a special case,when Layla and Majnun have equal feelings,we propose an analysis of the system in view of its equilibrium and fixed point sets.Considering that the system has marginal stability if its eigenvalues have both negative and zero real portions,it is demonstrated that the system neither converges nor diverges to a steady trajectory or equilibrium point.It,rather,continues to hover along the line separating stability and instability based on the fractional LMM system.
文摘This paper presents both analytical and numerical studies of the conservative Sawada-Kotera equation and its dissipative generalization,equations known for their soliton solutions and rich chaotic dynamics.These models offer valuable insights into nonlinear wave propagation,with applications in fluid dynamics and materials science,including systems such as liquid crystals and ferrofluids.It is shown that the conservative Sawada-Kotera equation supports traveling wave solutions corresponding to elliptic limit cycles,as well as two-and three-dimensional invariant tori surrounding these cycles in the associated ordinary differential equation(ODE)system.For the dissipative generalized Sawada-Kotera equation,chaotic wave behavior is observed.The transition to chaos in the corresponding ODE systemfollows a universal bifurcation scenario consistent with the framework established by FShM(Feigenbaum-Sharkovsky-Magnitskii)theory.Notably,this study demonstrates for the first time that the conservative Sawada-Kotera equation can exhibit complex quasi-periodic wave solutions,while its dissipative counterpart admits an infinite number of stable periodic and chaotic waveforms.
文摘The methods to determine time delays and embedding dimensions in the phase space delay reconstruction of multivariate chaotic time series are proposed. Three nonlinear prediction methods of multivariate chaotic time series including local mean prediction, local linear prediction and BP neural networks prediction are considered. The simulation results obtained by the Lorenz system show that no matter what nonlinear prediction method is used, the prediction error of multivariate chaotic time series is much smaller than the prediction error of univariate time series, even if half of the data of univariate time series are used in multivariate time series. The results also verify that methods to determine the time delays and the embedding dimensions are correct from the view of minimizing the prediction error.
文摘The chaotic dynamic behaviors of a reduction of perturbed Korteweg-de Vries （KdV） equation in form of a parametric excitation are studied. Chaotic behaviors from homoclinic crossings are analyzed with an improved Melnikov method and are compared for the systems with a periodically external excitation, with a linear periodically parametric excitation, or with a nonlinear periodically excitation. The critical curves separating chaotic regions and non-chaotic regions of the above systems are different from each other. Especially, a dead frequency is presented for the system with a nonlinear periodically parametric excitation. The chaos excited at the frequency does not occur no matter how large the excitation amplitude is. A time integration scheme is used to find the numerical solutions of these systems. Numerical results agree with the analytical ones.
