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
This paper investigates the chaos synchronisation between two coupled chaotic Chua＇s circuits. The sufficient condition presented by linear matrix inequalities （LMIs） of global asymptotic synchronisation is attaine...This paper investigates the chaos synchronisation between two coupled chaotic Chua＇s circuits. The sufficient condition presented by linear matrix inequalities （LMIs） of global asymptotic synchronisation is attained based on piecewise quadratic Lyapunov functions. First, we obtain the piecewise linear differential inclusions （pwLDIs） model of synchronisation error dynamics, then we design a switching （piecewise-linear） feedback control law to stabilise it based on the piecewise quadratic Laypunov functions. Then we give some numerical simulations to demonstrate the effectiveness of our theoretical results.展开更多
The eigenvalue space of the canonical four-dimensional Chua＇s circuit which can realize every eigenvalue for fourdimensional system is studied in this paper. First, the analytical relations between the circuit parame...The eigenvalue space of the canonical four-dimensional Chua＇s circuit which can realize every eigenvalue for fourdimensional system is studied in this paper. First, the analytical relations between the circuit parameters and the eigenvalues of the system are established, and therefore all the circuit parameters can be determined explicitly by any given set of eigenvalues. Then, the eigenvalue space of the circuit is investigated in two cases by the nonlinear elements used. According to the types of the eigenvalues, some novel hyperchaotic attractors are presented. Further, the dynamic behaviours of the circuit are studied by the bifurcation diagrams and the Lyapunov spectra of the eigenvalues.展开更多
Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme. In this paper, a non-fragile linear feedback control strategy with multipl...Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme. In this paper, a non-fragile linear feedback control strategy with multiplicative controller gain uncertainties is proposed for realizing the mixed-synchronization of Chua＇s circuits connected in a drive-response configuration. In particular, in the mixed-synchronization regime, different state variables of the response system can evolve into complete synchronization, anti-synchronization and even amplitude death simultaneously with the drive variables for an appropriate choice of scaling matrix. Using Lyapunov stability theory, we derive some sufficient criteria for achieving global mixed-synchronization. It is shown that the desired non-fragile state feedback controller can be constructed by solving a set of linear matrix inequalities （LMIs）. Numerical simulations are also provided to demonstrate the effectiveness of the proposed control approach.展开更多
This paper considers the chaos synchronization of the modified Chua 's circuit with x|x| function. We firstly show that a couple of the modified Chua systems with different parameters and initial conditions can be...This paper considers the chaos synchronization of the modified Chua 's circuit with x|x| function. We firstly show that a couple of the modified Chua systems with different parameters and initial conditions can be synchronized using active control when the values of parameters both in drive system and response system are known aforehand.Furthermore, based on Lyapunov stability theory we propose an adaptive active control approach to make the states of two identical Chua systems with unknown constant parameters asymptotically synchronized. Moreover the designed controller is independent of those unknown parameters. Numerical simulations are given to validate the proposed synchronization approach.展开更多
Based on the α-β bifurcation curves and the special characteristics of chaotic spectrum of chua’s circuit, this paper presents here a method for designing a Chua’s circuit which approximately satisfy specified spe...Based on the α-β bifurcation curves and the special characteristics of chaotic spectrum of chua’s circuit, this paper presents here a method for designing a Chua’s circuit which approximately satisfy specified spectrum distribution range.展开更多
The ultimate proof of our understanding of nature and engineering systems is reflected in our ability to control them.Since fractional calculus is more universal, we bring attention to the controllability of fractiona...The ultimate proof of our understanding of nature and engineering systems is reflected in our ability to control them.Since fractional calculus is more universal, we bring attention to the controllability of fractional order systems. First,we extend the conventional controllability theorem to the fractional domain. Strictly mathematical analysis and proof are presented. Because Chua＇s circuit is a typical representative of nonlinear circuits, we study the controllability of the fractional order Chua＇s circuit in detail using the presented theorem. Numerical simulations and theoretical analysis are both presented, which are in agreement with each other.展开更多
Chua＇s circuit is a well-known nonlinear electronic model, having complicated nonsmooth dynamic behaviors. The stability and boundary equilibrium bifurcations for a modified Chua＇s circuit system with the smooth deg...Chua＇s circuit is a well-known nonlinear electronic model, having complicated nonsmooth dynamic behaviors. The stability and boundary equilibrium bifurcations for a modified Chua＇s circuit system with the smooth degree of 3 are studied. The parametric areas of stability are specified in detail. It is found that the bifurcation graphs of the su- percritical and irregular pitchfork bifurcations are similar to those of the piecewise-smooth continuous （PWSC） systems caused by piecewise smoothness. However, the bifurcation graph of the supercritical Hopf bifurcation is similar to those of smooth systems. There- fore, the boundary equilibrium bifurcations of the non-smooth systems with the smooth degree of 3 should receive more attention due to their special features.展开更多
Instead of avoiding occurrence of chaos in motor drives, chaos is positively utilized in this paper. A new chaotic pulse width modulation （PWM） scheme is proposed and implemented for AC motors, which functions to si...Instead of avoiding occurrence of chaos in motor drives, chaos is positively utilized in this paper. A new chaotic pulse width modulation （PWM） scheme is proposed and implemented for AC motors, which functions to significantly suppress harmonic peaks and hence acoustic noise. The key is to employ the Chua＇s circuit for generating a desired chaotic sequence. By using a practical induction motor, computer simulation and experimental results verify that the chaotic PWM has advantages of harmonic peak suppression and simple hardware implementation over the conventional PWM and random PWM.展开更多
Chaos synchronization has been applied in secure communication, chemicalreaction, biological systems, and information processing. A new theorem to synchronization ofunified chaotic systems via adaptive control is prop...Chaos synchronization has been applied in secure communication, chemicalreaction, biological systems, and information processing. A new theorem to synchronization ofunified chaotic systems via adaptive control is proposed. The constructive theorem provides thedesign scheme for adaptive controller such that a respond system can synchronize with respect to anuncertain drive system. One example for discontinuous chaotic system is proposed to illustrate theeffectiveness and feasibility.展开更多
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.
基金Project partially supported by the grant from the Research Grants Council of the Hong Kong Special Administrative Region,China (Grant No. 101005)the National Natural Science Foundation of China (Grant No. 60904004)the Key Youth Science and Technology Foundation of University of Electronic Science and Technology of China (Grant No. L08010201JX0720)
文摘This paper investigates the chaos synchronisation between two coupled chaotic Chua＇s circuits. The sufficient condition presented by linear matrix inequalities （LMIs） of global asymptotic synchronisation is attained based on piecewise quadratic Lyapunov functions. First, we obtain the piecewise linear differential inclusions （pwLDIs） model of synchronisation error dynamics, then we design a switching （piecewise-linear） feedback control law to stabilise it based on the piecewise quadratic Laypunov functions. Then we give some numerical simulations to demonstrate the effectiveness of our theoretical results.
基金Project supported by the National Natural Science Foundation of China (Grant No. 50877007)
文摘The eigenvalue space of the canonical four-dimensional Chua＇s circuit which can realize every eigenvalue for fourdimensional system is studied in this paper. First, the analytical relations between the circuit parameters and the eigenvalues of the system are established, and therefore all the circuit parameters can be determined explicitly by any given set of eigenvalues. Then, the eigenvalue space of the circuit is investigated in two cases by the nonlinear elements used. According to the types of the eigenvalues, some novel hyperchaotic attractors are presented. Further, the dynamic behaviours of the circuit are studied by the bifurcation diagrams and the Lyapunov spectra of the eigenvalues.
基金Project supported by the Foundation for Distinguished Young Talents in Higher Education of Guangdong Province of China(Grant No. LYM10074)the Natural Science Foundation of Guangdong Province,China (Grant No. 9451042001004076)
文摘Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme. In this paper, a non-fragile linear feedback control strategy with multiplicative controller gain uncertainties is proposed for realizing the mixed-synchronization of Chua＇s circuits connected in a drive-response configuration. In particular, in the mixed-synchronization regime, different state variables of the response system can evolve into complete synchronization, anti-synchronization and even amplitude death simultaneously with the drive variables for an appropriate choice of scaling matrix. Using Lyapunov stability theory, we derive some sufficient criteria for achieving global mixed-synchronization. It is shown that the desired non-fragile state feedback controller can be constructed by solving a set of linear matrix inequalities （LMIs）. Numerical simulations are also provided to demonstrate the effectiveness of the proposed control approach.
文摘This paper considers the chaos synchronization of the modified Chua 's circuit with x|x| function. We firstly show that a couple of the modified Chua systems with different parameters and initial conditions can be synchronized using active control when the values of parameters both in drive system and response system are known aforehand.Furthermore, based on Lyapunov stability theory we propose an adaptive active control approach to make the states of two identical Chua systems with unknown constant parameters asymptotically synchronized. Moreover the designed controller is independent of those unknown parameters. Numerical simulations are given to validate the proposed synchronization approach.
文摘Based on the α-β bifurcation curves and the special characteristics of chaotic spectrum of chua’s circuit, this paper presents here a method for designing a Chua’s circuit which approximately satisfy specified spectrum distribution range.
基金supported by the National Natural Science Foundation of China(Grant Nos.51109180 and 51479173)the Fundamental Research Funds for the Central Universities,China(Grant No.201304030577)+1 种基金the Northwest A&F University Foundation,China(Grant No.2013BSJJ095)the Scientific Research Foundation on Water Engineering of Shaanxi Province,China(Grant No.2013slkj-12)
文摘The ultimate proof of our understanding of nature and engineering systems is reflected in our ability to control them.Since fractional calculus is more universal, we bring attention to the controllability of fractional order systems. First,we extend the conventional controllability theorem to the fractional domain. Strictly mathematical analysis and proof are presented. Because Chua＇s circuit is a typical representative of nonlinear circuits, we study the controllability of the fractional order Chua＇s circuit in detail using the presented theorem. Numerical simulations and theoretical analysis are both presented, which are in agreement with each other.
基金supported by the National Natural Science Foundation of China(Nos.U1204106,11372282,11272024,and 11371046)the National Basic Research Program of China(973 Program)(Nos.2012CB821200 and 2012CB821202)
文摘Chua＇s circuit is a well-known nonlinear electronic model, having complicated nonsmooth dynamic behaviors. The stability and boundary equilibrium bifurcations for a modified Chua＇s circuit system with the smooth degree of 3 are studied. The parametric areas of stability are specified in detail. It is found that the bifurcation graphs of the su- percritical and irregular pitchfork bifurcations are similar to those of the piecewise-smooth continuous （PWSC） systems caused by piecewise smoothness. However, the bifurcation graph of the supercritical Hopf bifurcation is similar to those of smooth systems. There- fore, the boundary equilibrium bifurcations of the non-smooth systems with the smooth degree of 3 should receive more attention due to their special features.
基金Project supported by the Shanghai Leading Academic Discipline Project (Grant No.T0103)
文摘Instead of avoiding occurrence of chaos in motor drives, chaos is positively utilized in this paper. A new chaotic pulse width modulation （PWM） scheme is proposed and implemented for AC motors, which functions to significantly suppress harmonic peaks and hence acoustic noise. The key is to employ the Chua＇s circuit for generating a desired chaotic sequence. By using a practical induction motor, computer simulation and experimental results verify that the chaotic PWM has advantages of harmonic peak suppression and simple hardware implementation over the conventional PWM and random PWM.
基金This project is jointly supported by the National Natural Science Foundation of China(No.60074034,No.70271068),the Research Fund for the Doctoral Program of Higher Education(No.200020008004)and the Foundation for University Key Teacher by the Ministry of
文摘Chaos synchronization has been applied in secure communication, chemicalreaction, biological systems, and information processing. A new theorem to synchronization ofunified chaotic systems via adaptive control is proposed. The constructive theorem provides thedesign scheme for adaptive controller such that a respond system can synchronize with respect to anuncertain drive system. One example for discontinuous chaotic system is proposed to illustrate theeffectiveness and feasibility.
