This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fra...This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fractal dimension and the hyperchaotic attractor evolving into chaotic, periodic, quasi-periodic dynamical behaviours by varying parameter d are studied briefly. Various attractors are illustrated not only by computer simulation but also by conducting an electronic circuit experiment.展开更多
Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperc...Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperchaotic Liu system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyperchaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the two new systems are studied, respectively. Furthermore, the synchronizing circuits of the nonautonomous hyperchaotic Liu system are designed via the synchronization control method of single variable coupling feedback. Finally, the hardware circuits are implemented, and the corresponding waves of chaos are observed by an oscillograph.展开更多
The chaotic motion behavior of the rectangular conductive thin plate that is simply supported on four sides by airflow andmechanical external excitation in a magnetic field is studied.According to Kirchhoff’s thin pl...The chaotic motion behavior of the rectangular conductive thin plate that is simply supported on four sides by airflow andmechanical external excitation in a magnetic field is studied.According to Kirchhoff’s thin plate theory,considering geometric nonlinearity and using the principle of virtualwork,the nonlinearmotion partial differential equation of the rectangular conductive thin plate is deduced.Using the separate variable method and Galerkin’s method,the system motion partial differential equation is converted into the general equation of the Duffing equation;the Hamilton system is introduced,and the Melnikov function is used to analyze the Hamilton system,and obtain the critical surface for the existence of chaos.The bifurcation diagram,phase portrait,time history response and Poincarémap of the vibration system are obtained by numerical simulation,and the correctness is demonstrated.The results showthatwhen the ratio of external excitation amplitude to damping coefficient is higher than the critical surface,the system will enter chaotic state.The chaotic motion of the rectangular conductive thin plate is affected by different magnetic field distributions and airflow.展开更多
A kind of synchronization controller for Liu chaotic systems whose nonlinear components are subject to Lipschitz condition was proposed. By using Lyapunov function and linear matrix inequality technique, a self-adapti...A kind of synchronization controller for Liu chaotic systems whose nonlinear components are subject to Lipschitz condition was proposed. By using Lyapunov function and linear matrix inequality technique, a self-adaptive synchronization controller was constructed for Liu chaotic systems. There are two components of our derived synchronization controller: linear and nonlinear component. Linear component is composed of errors of the state variables between driving-systems and responding-stems, and nonlinear component is a self-adaptive synchronization controller. a proof was given for proving the feasibility of this method, and numerical simulations of Liu chaotic systems show its effectiveness. Furthermore, this method can be applied to other chaotic systems, such as Chen systems, Lorenz systems, Chua systems and Rssler systems,etc.展开更多
In the paper, the Liu system with a feedback controller is discussed. The influence of the feedback coefficient of the controlled system is studied through Lyapunov exponents spectrum and bifurcation diagram. Various ...In the paper, the Liu system with a feedback controller is discussed. The influence of the feedback coefficient of the controlled system is studied through Lyapunov exponents spectrum and bifurcation diagram. Various attractors are demonstrated not only by numerical simulations but also by circuit experiments. Only one feedback channel is used in our study, which is useful in communication. The circuit experiments show that our study has significance in practical applications.展开更多
This paper further investigates the synchronization problem of a new chaotic system with known or unknown system parameters. Based on the Lyapunov stability theory,a novel adaptive control law is derived for the synch...This paper further investigates the synchronization problem of a new chaotic system with known or unknown system parameters. Based on the Lyapunov stability theory,a novel adaptive control law is derived for the synchronization of a new chaotic system with known or unknown system parameters.Theoretical analysis and numerical simulations showthe effectiveness and feasibility of the proposed schemes.展开更多
The stability of impulsive fractional-order systems is discussed. A new synchronization criterion of fractional-order chaotic systems is proposed based on the stability theory of impulsive fractional-order systems. Th...The stability of impulsive fractional-order systems is discussed. A new synchronization criterion of fractional-order chaotic systems is proposed based on the stability theory of impulsive fractional-order systems. The synchronization criterion is suitable for the case of the order 0 〈 q ≤ 1. It is more general than those of the known results. Simulation results are given to show the effectiveness of the proposed synchronization criterion.展开更多
This research presents,and claries the application of two permutation algorithms,based on chaotic map systems,and applied to a le of speech signals.They are the Arnold cat map-based permutation algorithm,and the Baker...This research presents,and claries the application of two permutation algorithms,based on chaotic map systems,and applied to a le of speech signals.They are the Arnold cat map-based permutation algorithm,and the Baker’s chaotic map-based permutation algorithm.Both algorithms are implemented on the same speech signal sample.Then,both the premier and the encrypted le histograms are documented and plotted.The speech signal amplitude values with time signals of the original le are recorded and plotted against the encrypted and decrypted les.Furthermore,the original le is plotted against the encrypted le,using the spectrogram frequencies of speech signals with the signal duration.These permutation algorithms are used to shufe the positions of the speech les signals’values without any changes,to produce an encrypted speech le.A comparative analysis is introduced by using some of sundry statistical and experimental analyses for the procedures of encryption and decryption,e.g.,the time of both procedures,the encrypted audio signals histogram,the correlation coefcient between specimens in the premier and encrypted signals,a test of the Spectral Distortion(SD),and the Log-Likelihood Ratio(LLR)measures.The outcomes of the different experimental and comparative studies demonstrate that the two permutation algorithms(Baker and Arnold)are sufcient for providing an efcient and reliable voice signal encryption solution.However,the Arnold’s algorithm gives better results in most cases as compared to the results of Baker’s algorithm.展开更多
Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view.In this work,we present a numerical investigation of a novel approach,known as the space-split sensitivity or ...Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view.In this work,we present a numerical investigation of a novel approach,known as the space-split sensitivity or S3 algorithm.The S3 algorithm is an ergodic-averaging method to differentiate statistics in ergodic,chaotic systems,rigorously based on the theory of hyperbolic dynamics.We illustrate S3 on one-dimensional chaotic maps,revealing its computational advantage over na?ve finite difference computations of the same statistical response.In addition,we provide an intuitive explanation of the key components of the S3 algorithm,including the density gradient function.展开更多
A technical framework of constructing a linear controller for chaotic synchronization by utilizing the stability theory of cascade-connected system is presented. Based on the method developed in the paper, two simple ...A technical framework of constructing a linear controller for chaotic synchronization by utilizing the stability theory of cascade-connected system is presented. Based on the method developed in the paper, two simple and linear feedback controllers, as examples, are derived for the synchronization of Liu chaotic system and Duffing oscillator, respectively. This method is quite flexible in constructing a control law. Its effectiveness is also illustrated by the simulation results.展开更多
Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based o...Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based on Lya-punov's stability theory, linear and nonlinear feedback control of adaptive H∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an Hoe-norm constraint. Adaptive H∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems. Numerical simulations are also given to identify the effectiveness of the theoretical analysis.展开更多
Least-square support vector machines(LS-SVM) are applied for learning the chaotic behavior of Chua's circuit.The system is divided into three multiple-input single-output(MISO) structures and the LS-SVM are train...Least-square support vector machines(LS-SVM) are applied for learning the chaotic behavior of Chua's circuit.The system is divided into three multiple-input single-output(MISO) structures and the LS-SVM are trained individually.Comparing with classical approaches,the proposed one reduces the structural complexity and the selection of parameters is avoided.Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation.Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua's circuit state variables,and exhibit the chaotic attractors under the autonomous working mode.展开更多
Hurst’s memory that roots in early work of the British hydrologist H.E. Hurst remains an open problem in stochastic hydrology. Today, the Hurst analysis is widely used for the hydrological studies for the memory and ...Hurst’s memory that roots in early work of the British hydrologist H.E. Hurst remains an open problem in stochastic hydrology. Today, the Hurst analysis is widely used for the hydrological studies for the memory and characteristics of time series and many methodologies have been developed for the analysis. So, there are many different techniques for the estimation of the Hurst exponent (H). However, the techniques can produce different characteristics for the persistence of a time series each other. This study uses several techniques such as adjusted range, rescaled range (RR) analysis, modified rescaled range (MRR) analysis, 1/f power spectral density analysis, Maximum Likelihood Estimation (MLE), detrended fluctuations analysis (DFA), and aggregated variance time (AVT) method for the Hurst exponent estimation. The generated time series from chaos and stochastic systems are analyzed for the comparative study of the techniques. Then, this study discusses the advantages and disadvantages of the techniques and also the limitations of them. We found that DFA is the most appropriate technique for the Hurst exponent estimation for both the short term memory and long term memory. We analyze the SOI (Southern Oscillations Index) and 6 tree-ring series for USA sites by means of DFA and the BDS statistic is used for nonlinearity test of the series. From the results, we found that SOI series is nonlinear time series which has a long term memory of H = 0.92. Contrary to earlier work, all the tree ring series are not random from our analysis. A certain tree ring series show a long term memory of H = 0.97 and nonlinear property. Therefore, we can say that the SOI series has the properties of long memory and nonlinearity and tree ring series could also show long memory and non-linearity.展开更多
A substitution box (S-box) plays an important role in cryptographic algorithms.The design of S-box using chaotic systems has attracted a great deal of attention in recent years.A new method for obtaining cryptographic...A substitution box (S-box) plays an important role in cryptographic algorithms.The design of S-box using chaotic systems has attracted a great deal of attention in recent years.A new method for obtaining cryptographically strong S-boxes based on spatiotemporal chaotic system is proposed in this paper.The discretized Baker map and affine transformation are used orderly by an algorithm to shuffle the table generated by the spatiotemporal chaotic system.The cryptographical properties of these S-boxes such as bijection,nonlinearity,strict avalanche,output bits independence and equiprobable input /output XOR distribution are analyzed.The results of numerical analysis show that the S-box designed by this method can against several attacks and all the criteria for designing good S-box can be satisfied approximately.More strong S-boxes can be obtained by this method with the change of the original conditions or control parameters of the spatiotemporal chaos system.Furthermore,our approach is suitable for practical application in designing cryptosystem.展开更多
Asthma is characterized by paroxysmaldyspnea,rales in the throat,difficulty in breathing,and inability to lie horizontally.It is commonly seenin children with a weak body constitution,and tendsto be intractable,thus b...Asthma is characterized by paroxysmaldyspnea,rales in the throat,difficulty in breathing,and inability to lie horizontally.It is commonly seenin children with a weak body constitution,and tendsto be intractable,thus being harmful to the展开更多
文摘This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fractal dimension and the hyperchaotic attractor evolving into chaotic, periodic, quasi-periodic dynamical behaviours by varying parameter d are studied briefly. Various attractors are illustrated not only by computer simulation but also by conducting an electronic circuit experiment.
基金Project supported by the National Natural Science Foundation of China (Grant No 60572089)the Natural Science Foundation of Chongqing (Grant No CSTC,2008BB2087)
文摘Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperchaotic Liu system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyperchaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the two new systems are studied, respectively. Furthermore, the synchronizing circuits of the nonautonomous hyperchaotic Liu system are designed via the synchronization control method of single variable coupling feedback. Finally, the hardware circuits are implemented, and the corresponding waves of chaos are observed by an oscillograph.
基金funded by the Anhui Provincial Natural Science Foundation(Grant No.2008085QE245)the Natural Science Research Project of Higher Education Institutions in Anhui Province(2022AH040045)the Project of Science and Technology Plan of Department of Housing and Urban-Rural Development of Anhui Province(2021-YF22).
文摘The chaotic motion behavior of the rectangular conductive thin plate that is simply supported on four sides by airflow andmechanical external excitation in a magnetic field is studied.According to Kirchhoff’s thin plate theory,considering geometric nonlinearity and using the principle of virtualwork,the nonlinearmotion partial differential equation of the rectangular conductive thin plate is deduced.Using the separate variable method and Galerkin’s method,the system motion partial differential equation is converted into the general equation of the Duffing equation;the Hamilton system is introduced,and the Melnikov function is used to analyze the Hamilton system,and obtain the critical surface for the existence of chaos.The bifurcation diagram,phase portrait,time history response and Poincarémap of the vibration system are obtained by numerical simulation,and the correctness is demonstrated.The results showthatwhen the ratio of external excitation amplitude to damping coefficient is higher than the critical surface,the system will enter chaotic state.The chaotic motion of the rectangular conductive thin plate is affected by different magnetic field distributions and airflow.
基金supported by the Science Foundation of Chongqing Education Department(KJ060506)Doctor Foundation of Chongqing University of Posts and Telecommunications(A2006-85)
文摘A kind of synchronization controller for Liu chaotic systems whose nonlinear components are subject to Lipschitz condition was proposed. By using Lyapunov function and linear matrix inequality technique, a self-adaptive synchronization controller was constructed for Liu chaotic systems. There are two components of our derived synchronization controller: linear and nonlinear component. Linear component is composed of errors of the state variables between driving-systems and responding-stems, and nonlinear component is a self-adaptive synchronization controller. a proof was given for proving the feasibility of this method, and numerical simulations of Liu chaotic systems show its effectiveness. Furthermore, this method can be applied to other chaotic systems, such as Chen systems, Lorenz systems, Chua systems and Rssler systems,etc.
文摘In the paper, the Liu system with a feedback controller is discussed. The influence of the feedback coefficient of the controlled system is studied through Lyapunov exponents spectrum and bifurcation diagram. Various attractors are demonstrated not only by numerical simulations but also by circuit experiments. Only one feedback channel is used in our study, which is useful in communication. The circuit experiments show that our study has significance in practical applications.
文摘This paper further investigates the synchronization problem of a new chaotic system with known or unknown system parameters. Based on the Lyapunov stability theory,a novel adaptive control law is derived for the synchronization of a new chaotic system with known or unknown system parameters.Theoretical analysis and numerical simulations showthe effectiveness and feasibility of the proposed schemes.
基金supported by Scientific Research Foundation of Huaiyin Institute of Technology (Grant No. HGA1102)
文摘The stability of impulsive fractional-order systems is discussed. A new synchronization criterion of fractional-order chaotic systems is proposed based on the stability theory of impulsive fractional-order systems. The synchronization criterion is suitable for the case of the order 0 〈 q ≤ 1. It is more general than those of the known results. Simulation results are given to show the effectiveness of the proposed synchronization criterion.
文摘This research presents,and claries the application of two permutation algorithms,based on chaotic map systems,and applied to a le of speech signals.They are the Arnold cat map-based permutation algorithm,and the Baker’s chaotic map-based permutation algorithm.Both algorithms are implemented on the same speech signal sample.Then,both the premier and the encrypted le histograms are documented and plotted.The speech signal amplitude values with time signals of the original le are recorded and plotted against the encrypted and decrypted les.Furthermore,the original le is plotted against the encrypted le,using the spectrogram frequencies of speech signals with the signal duration.These permutation algorithms are used to shufe the positions of the speech les signals’values without any changes,to produce an encrypted speech le.A comparative analysis is introduced by using some of sundry statistical and experimental analyses for the procedures of encryption and decryption,e.g.,the time of both procedures,the encrypted audio signals histogram,the correlation coefcient between specimens in the premier and encrypted signals,a test of the Spectral Distortion(SD),and the Log-Likelihood Ratio(LLR)measures.The outcomes of the different experimental and comparative studies demonstrate that the two permutation algorithms(Baker and Arnold)are sufcient for providing an efcient and reliable voice signal encryption solution.However,the Arnold’s algorithm gives better results in most cases as compared to the results of Baker’s algorithm.
基金supported by the Air Force Office of Scientific Research(Grant FA8650-19-C-2207)。
文摘Sensitivity analysis in chaotic dynamical systems is a challenging task from a computational point of view.In this work,we present a numerical investigation of a novel approach,known as the space-split sensitivity or S3 algorithm.The S3 algorithm is an ergodic-averaging method to differentiate statistics in ergodic,chaotic systems,rigorously based on the theory of hyperbolic dynamics.We illustrate S3 on one-dimensional chaotic maps,revealing its computational advantage over na?ve finite difference computations of the same statistical response.In addition,we provide an intuitive explanation of the key components of the S3 algorithm,including the density gradient function.
基金Project supported by the National Natural Science Foundation of China (Grant No 60274032) and the Science and Technology Rising-Star Program of Shanghai (Grant No 04QMH1405).
文摘A technical framework of constructing a linear controller for chaotic synchronization by utilizing the stability theory of cascade-connected system is presented. Based on the method developed in the paper, two simple and linear feedback controllers, as examples, are derived for the synchronization of Liu chaotic system and Duffing oscillator, respectively. This method is quite flexible in constructing a control law. Its effectiveness is also illustrated by the simulation results.
文摘Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated. The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach. Based on Lya-punov's stability theory, linear and nonlinear feedback control of adaptive H∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an Hoe-norm constraint. Adaptive H∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems. Numerical simulations are also given to identify the effectiveness of the theoretical analysis.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61072103)the Jiangxi Province Training Program for Younger Scientists
文摘Least-square support vector machines(LS-SVM) are applied for learning the chaotic behavior of Chua's circuit.The system is divided into three multiple-input single-output(MISO) structures and the LS-SVM are trained individually.Comparing with classical approaches,the proposed one reduces the structural complexity and the selection of parameters is avoided.Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation.Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua's circuit state variables,and exhibit the chaotic attractors under the autonomous working mode.
文摘Hurst’s memory that roots in early work of the British hydrologist H.E. Hurst remains an open problem in stochastic hydrology. Today, the Hurst analysis is widely used for the hydrological studies for the memory and characteristics of time series and many methodologies have been developed for the analysis. So, there are many different techniques for the estimation of the Hurst exponent (H). However, the techniques can produce different characteristics for the persistence of a time series each other. This study uses several techniques such as adjusted range, rescaled range (RR) analysis, modified rescaled range (MRR) analysis, 1/f power spectral density analysis, Maximum Likelihood Estimation (MLE), detrended fluctuations analysis (DFA), and aggregated variance time (AVT) method for the Hurst exponent estimation. The generated time series from chaos and stochastic systems are analyzed for the comparative study of the techniques. Then, this study discusses the advantages and disadvantages of the techniques and also the limitations of them. We found that DFA is the most appropriate technique for the Hurst exponent estimation for both the short term memory and long term memory. We analyze the SOI (Southern Oscillations Index) and 6 tree-ring series for USA sites by means of DFA and the BDS statistic is used for nonlinearity test of the series. From the results, we found that SOI series is nonlinear time series which has a long term memory of H = 0.92. Contrary to earlier work, all the tree ring series are not random from our analysis. A certain tree ring series show a long term memory of H = 0.97 and nonlinear property. Therefore, we can say that the SOI series has the properties of long memory and nonlinearity and tree ring series could also show long memory and non-linearity.
基金Sponsored by the National Natural Science Foundation of China(Grant No.61074192)the Beijing Natural Science Foundation(Grant No.4092040)the Natural Science Research of Henan Province Education Department(Grant No.2011B110002)
文摘A substitution box (S-box) plays an important role in cryptographic algorithms.The design of S-box using chaotic systems has attracted a great deal of attention in recent years.A new method for obtaining cryptographically strong S-boxes based on spatiotemporal chaotic system is proposed in this paper.The discretized Baker map and affine transformation are used orderly by an algorithm to shuffle the table generated by the spatiotemporal chaotic system.The cryptographical properties of these S-boxes such as bijection,nonlinearity,strict avalanche,output bits independence and equiprobable input /output XOR distribution are analyzed.The results of numerical analysis show that the S-box designed by this method can against several attacks and all the criteria for designing good S-box can be satisfied approximately.More strong S-boxes can be obtained by this method with the change of the original conditions or control parameters of the spatiotemporal chaos system.Furthermore,our approach is suitable for practical application in designing cryptosystem.
文摘Asthma is characterized by paroxysmaldyspnea,rales in the throat,difficulty in breathing,and inability to lie horizontally.It is commonly seenin children with a weak body constitution,and tendsto be intractable,thus being harmful to the