We present a new method for generating multiple-scroll attractors. By constructing a piece-wise-linear odd function as the driving-point characteristic of Chua's diode with multiple breakpoints, and finding a recu...We present a new method for generating multiple-scroll attractors. By constructing a piece-wise-linear odd function as the driving-point characteristic of Chua's diode with multiple breakpoints, and finding a recurrence formula for determining equilibrium point voltages and breakpoint voltages, we can calculate the voltages of all the equilibrium points and breakpoints, and the multiple-scroll chaotic attractors can be obtained. This method is based on Shil'nikov theorem and the cell model of chaotic attractors. The theoretical calculations are in good agreement with computer simulations and hardware experimental results. Compared with the results reported by Suykens, our method has some advantages that much more scrolls can be obtained, the scrolls are uniform in size, and a general recurrence formula for generating attractors with any number of scrolls is given. Furthermore, the observation of attractors with a maximum of 11-21 uniform scrolls obtained by hardware experiment and computer simulation, respectively, is reported for the first time.展开更多
The synchronization of Chua＇s system, whose inputs include an unknown constant parameter, is studied in this paper. A constructive method is applied to designing an adaptive controller, in which only one variable inf...The synchronization of Chua＇s system, whose inputs include an unknown constant parameter, is studied in this paper. A constructive method is applied to designing an adaptive controller, in which only one variable information of the master system is needed. With the action of control signals, the parameter of the slave system will approach the corresponding unknown parameter in the master system. At the same time, the synchronization errors will also converge to zero asymptotically. Numerical simulations show that the proposed theoretical approach is very effective.展开更多
The qualitative solutions of dynamical system expressed with nonlinear differential equation can be divided into two categories. One is that the motion of phase point may approach infinite or stable equilibrium point ...The qualitative solutions of dynamical system expressed with nonlinear differential equation can be divided into two categories. One is that the motion of phase point may approach infinite or stable equilibrium point eventually. Neither periodic excited source nor self-excited oscillation exists in such nonlinear dynamic circuits, so its solution cannot be treated as the synthesis of multiharmonic. And the other is that the endless vibration of phase point is limited within certain range, moreover possesses character of sustained oscillation, namely the bounded nonlinear oscillation. It can persistently and repeatedly vibration after dynamic variable entering into steady state;moreover the motion of phase point will not approach infinite at last;system has not stable equilibrium point. The motional trajectory can be described by a bounded space curve. So far, the curve cannot be represented by concretely explicit parametric form in math. It cannot be expressed analytically by human. The chaos is a most universally common form of bounded nonlinear oscillation. A number of chaotic systems, such as Lorenz equation, Chua’s circuit and lossless system in modern times are some examples among thousands of chaotic equations. In this work, basic properties related to the bounded space curve will be comprehensively summarized by analyzing these examples.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
P This paper studies how phase synchronization in complex networks depends on random shortcuts, using the uous chaotic Chua system as the nodes of the networks. It is found that for a given coupling strength when the ...P This paper studies how phase synchronization in complex networks depends on random shortcuts, using the uous chaotic Chua system as the nodes of the networks. It is found that for a given coupling strength when the number of random shortcuts is greater than a threshold the phase synchronization is induced. Phase synchronization becomes evident and reaches its maximum as the number of random shortcuts is further increased. These phenomena imply that random shortcuts can induce and enhance the phase synchronization in complex Chua systems. Furthermore, the paper also investigates the effects of the coupling strength and it is found that stronger coupling makes it easier to obtain the complete phase synchronization.展开更多
Some new criteria for the chaotic lag synchronization are proposed. At first,lag synchronization scheme for identical master-slave Lur‘ e systems by replacing variables control and the relevant error system are given...Some new criteria for the chaotic lag synchronization are proposed. At first,lag synchronization scheme for identical master-slave Lur‘ e systems by replacing variables control and the relevant error system are given, and the relations between absolute stability of the error system and the chaotic lag synchronization are described. Then, based on a quadratic Lyapunov function, two new Lur‘ e criteria for the above chaotic lag synchronization are proved. Four corresponding frequency domain criteria are further derived by means of Meyer-Kalman-Yacubovia Lemma. These frequency domain criteria are applied to analyze the lag synchronization of general master-slave Chua's circuits so that some ranges of the parameters in which the master-slave Chua's circuits achieve chaotic lag synchronization by replacing single-variable control are attained. Finally, some examples are given to verify the theoretical results.展开更多
A novel framework for chaos and its impul-sive control in Chua＇s oscillator via time-delay feedback is presented.The exponential stability of impulsive control Chua＇s oscillator via time-delay feedback is considered...A novel framework for chaos and its impul-sive control in Chua＇s oscillator via time-delay feedback is presented.The exponential stability of impulsive control Chua＇s oscillator via time-delay feedback is considered,and some novel conditions are obtained.Then a novel impulsive controller design procedure is proposed.Simulation experiments are provided to demonstrate the feasibility and effectiveness of our method finally.展开更多
A robust adaptive fuzzy control scheme is presented for a class of strict-feedback nonaffine nonlinear systems with modeling uncertainties and external disturbances by using a backstepping approach.Fuzzy logic systems...A robust adaptive fuzzy control scheme is presented for a class of strict-feedback nonaffine nonlinear systems with modeling uncertainties and external disturbances by using a backstepping approach.Fuzzy logic systems are employed to approximate the unknown parts of the desired virtual controls,and the approximation errors of fuzzy systems are only required to be norm-bounded.The function tanh（·） is introduced to avoid problems associated with sgn（·）.The tracking error is guaranteed to be uniformly ultimately bounded with the aid of an additional adaptive compensation term.Chua＇s circuit system and R o¨ssler system are presented to illustrate the feasibility and effectiveness of the proposed control technique.展开更多
Chua＇s circuit, which is improved to integrate conveniently, is presented. A drive-response chaotic synchronization system is constructed, which possesses a certain stability, resisting-disturbance, and so on. By mea...Chua＇s circuit, which is improved to integrate conveniently, is presented. A drive-response chaotic synchronization system is constructed, which possesses a certain stability, resisting-disturbance, and so on. By means of research, it can be concluded that the chaotic synchronization system is provided with the characteristic of chaos synchronization self-maintenance. Utilizing the characteristic, the critical problem of how to simultaneously transmit the controlling signal of chaotic synchronization and the secret signal at a channel can be solved, and that a practical experiment validates the method; as a result, the research in the paper provides the foundation of putting chaos into practice application to secret communication.展开更多
Presents analytic criteria for the local activity theory in two-port cellularneural network (CNN) cells with four local state variables, and gives the application to a smoothedChua's circuit (SCC) CNN with two-por...Presents analytic criteria for the local activity theory in two-port cellularneural network (CNN) cells with four local state variables, and gives the application to a smoothedChua's circuit (SCC) CNN with two-port and I 5 S 15 arrays. The bifurcation diagrams of the SCC CNNshow that they are completely the same as those of an SCC CNN with one-port calculated earlier;which do not exist locally passive domain. The evolution of the patterns of the state variables ofthe SCC CNN is stimulated. Oscillatory patterns, chaotic patterns, or divergent patterns may emergeif the selected cell parameters are located in the locally active unstable domains but nearby theedge of chaos domain.展开更多
The analytic criteria for the local activity theory in one-port cellularneural network (CNN) with five local state variables are presented. The application to a Hyper-chaossynchronization Chua's circuit (HCSCC) CN...The analytic criteria for the local activity theory in one-port cellularneural network (CNN) with five local state variables are presented. The application to a Hyper-chaossynchronization Chua's circuit (HCSCC) CNN with 1125 variables is studied. The bifurcation diagramsof the HCSCC CNN show that they are slightly different from the smoothed CNN with one or two portsand four state variables calculated earlier. The evolution of the patterns of the state variables ofthe HCSCC CNN is stimulated. Oscillatory patterns, chaotic patterns, convergent or divergentpatterns may emerge if the selected cell parameters are located in the locally active domains butnearby or in the edge of chaos domain.展开更多
This paper studies chaos synchronization in the modified Chua ' s circuitwith nonlinear quadratic function x|x| using a unidirectional Linear coupling approach. A newsufficient condition is derived for chaos synch...This paper studies chaos synchronization in the modified Chua ' s circuitwith nonlinear quadratic function x|x| using a unidirectional Linear coupling approach. A newsufficient condition is derived for chaos synchronization between the two unidirectional coupledmodified Chua ' s circuits with x x I based on the Lyapunov stability theory. A simulation exampleis given for demonstration .展开更多
We introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry, especially in the frame of chaotic attractors for solving practical problems(generating ...We introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry, especially in the frame of chaotic attractors for solving practical problems(generating hyperchaos; developing chaos based pseudo random number generator(CPRNG) and chaotic multistream PRNG; secure communication via synchronization). They can also be used in cryptography, generic algorithms in optimization, control, etc.展开更多
Secure communication through chaos synchronization using small time continuous feedback is investigated. The factor K\-r>2 for guaranteeing good recovery of the information signal is determined. The simulation circ...Secure communication through chaos synchronization using small time continuous feedback is investigated. The factor K\-r>2 for guaranteeing good recovery of the information signal is determined. The simulation circuit experiment is given by PSPICE circuit simulator. Theory and experiment demonstrate that the secure communication by small time continuous feedback method does not require the system to be divided into subsystems, and has no limitation of signal to noise ratio.展开更多
In this paper, a new type of chaos shift keying(CSK) modulation, called multi state CSK, is analyzed and tested. In this type of modulation combined with feedback synchronization, the data rate can be greatly incre...In this paper, a new type of chaos shift keying(CSK) modulation, called multi state CSK, is analyzed and tested. In this type of modulation combined with feedback synchronization, the data rate can be greatly increased. Laboratory test results confirm very well with theoretical analysis.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
Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive an...Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua＇s circuit.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No.69672022)the Doctoral Education Foundation of China (Grant No. 00056107)the Natural Science Foundation of the Education Department of Guangdong Province (Grant No
文摘We present a new method for generating multiple-scroll attractors. By constructing a piece-wise-linear odd function as the driving-point characteristic of Chua's diode with multiple breakpoints, and finding a recurrence formula for determining equilibrium point voltages and breakpoint voltages, we can calculate the voltages of all the equilibrium points and breakpoints, and the multiple-scroll chaotic attractors can be obtained. This method is based on Shil'nikov theorem and the cell model of chaotic attractors. The theoretical calculations are in good agreement with computer simulations and hardware experimental results. Compared with the results reported by Suykens, our method has some advantages that much more scrolls can be obtained, the scrolls are uniform in size, and a general recurrence formula for generating attractors with any number of scrolls is given. Furthermore, the observation of attractors with a maximum of 11-21 uniform scrolls obtained by hardware experiment and computer simulation, respectively, is reported for the first time.
基金Project supported by the National Natural Science Foundation of China （Grant No 60502009）.
文摘The synchronization of Chua＇s system, whose inputs include an unknown constant parameter, is studied in this paper. A constructive method is applied to designing an adaptive controller, in which only one variable information of the master system is needed. With the action of control signals, the parameter of the slave system will approach the corresponding unknown parameter in the master system. At the same time, the synchronization errors will also converge to zero asymptotically. Numerical simulations show that the proposed theoretical approach is very effective.
文摘The qualitative solutions of dynamical system expressed with nonlinear differential equation can be divided into two categories. One is that the motion of phase point may approach infinite or stable equilibrium point eventually. Neither periodic excited source nor self-excited oscillation exists in such nonlinear dynamic circuits, so its solution cannot be treated as the synthesis of multiharmonic. And the other is that the endless vibration of phase point is limited within certain range, moreover possesses character of sustained oscillation, namely the bounded nonlinear oscillation. It can persistently and repeatedly vibration after dynamic variable entering into steady state;moreover the motion of phase point will not approach infinite at last;system has not stable equilibrium point. The motional trajectory can be described by a bounded space curve. So far, the curve cannot be represented by concretely explicit parametric form in math. It cannot be expressed analytically by human. The chaos is a most universally common form of bounded nonlinear oscillation. A number of chaotic systems, such as Lorenz equation, Chua’s circuit and lossless system in modern times are some examples among thousands of chaotic equations. In this work, basic properties related to the bounded space curve will be comprehensively summarized by analyzing these examples.
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.
基金Project supported by National Natural Science Foundation of China (Grant Nos 10862001 and 10647001)Guangxi Natural Science Foundation (Grant No 0728042)
文摘P This paper studies how phase synchronization in complex networks depends on random shortcuts, using the uous chaotic Chua system as the nodes of the networks. It is found that for a given coupling strength when the number of random shortcuts is greater than a threshold the phase synchronization is induced. Phase synchronization becomes evident and reaches its maximum as the number of random shortcuts is further increased. These phenomena imply that random shortcuts can induce and enhance the phase synchronization in complex Chua systems. Furthermore, the paper also investigates the effects of the coupling strength and it is found that stronger coupling makes it easier to obtain the complete phase synchronization.
基金This work was supported by the National Natural Science Foundation of China (No. 10371136)the Natural Science Foundation of Guangdong Province of China (No.021765).
文摘Some new criteria for the chaotic lag synchronization are proposed. At first,lag synchronization scheme for identical master-slave Lur‘ e systems by replacing variables control and the relevant error system are given, and the relations between absolute stability of the error system and the chaotic lag synchronization are described. Then, based on a quadratic Lyapunov function, two new Lur‘ e criteria for the above chaotic lag synchronization are proved. Four corresponding frequency domain criteria are further derived by means of Meyer-Kalman-Yacubovia Lemma. These frequency domain criteria are applied to analyze the lag synchronization of general master-slave Chua's circuits so that some ranges of the parameters in which the master-slave Chua's circuits achieve chaotic lag synchronization by replacing single-variable control are attained. Finally, some examples are given to verify the theoretical results.
文摘A novel framework for chaos and its impul-sive control in Chua＇s oscillator via time-delay feedback is presented.The exponential stability of impulsive control Chua＇s oscillator via time-delay feedback is considered,and some novel conditions are obtained.Then a novel impulsive controller design procedure is proposed.Simulation experiments are provided to demonstrate the feasibility and effectiveness of our method finally.
基金supported by the National Natural Science Foundation of China (9071602811001128)
文摘A robust adaptive fuzzy control scheme is presented for a class of strict-feedback nonaffine nonlinear systems with modeling uncertainties and external disturbances by using a backstepping approach.Fuzzy logic systems are employed to approximate the unknown parts of the desired virtual controls,and the approximation errors of fuzzy systems are only required to be norm-bounded.The function tanh（·） is introduced to avoid problems associated with sgn（·）.The tracking error is guaranteed to be uniformly ultimately bounded with the aid of an additional adaptive compensation term.Chua＇s circuit system and R o¨ssler system are presented to illustrate the feasibility and effectiveness of the proposed control technique.
基金the Special Scientific Research Program of Education Department of Shaanxi Province (Grant No. 05Jk159)
文摘Chua＇s circuit, which is improved to integrate conveniently, is presented. A drive-response chaotic synchronization system is constructed, which possesses a certain stability, resisting-disturbance, and so on. By means of research, it can be concluded that the chaotic synchronization system is provided with the characteristic of chaos synchronization self-maintenance. Utilizing the characteristic, the critical problem of how to simultaneously transmit the controlling signal of chaotic synchronization and the secret signal at a channel can be solved, and that a practical experiment validates the method; as a result, the research in the paper provides the foundation of putting chaos into practice application to secret communication.
基金This project is jointly supported by the National Nature Science Foundation of China (Grant No. 60074034) and the Foundation for
文摘Presents analytic criteria for the local activity theory in two-port cellularneural network (CNN) cells with four local state variables, and gives the application to a smoothedChua's circuit (SCC) CNN with two-port and I 5 S 15 arrays. The bifurcation diagrams of the SCC CNNshow that they are completely the same as those of an SCC CNN with one-port calculated earlier;which do not exist locally passive domain. The evolution of the patterns of the state variables ofthe SCC CNN is stimulated. Oscillatory patterns, chaotic patterns, or divergent patterns may emergeif the selected cell parameters are located in the locally active unstable domains but nearby theedge of chaos domain.
基金the National Natural Science Foundation of China (Grant No. 60074034) and the Foundation forUniversity Key Teacher by the Ministry of Education of China.
文摘The analytic criteria for the local activity theory in one-port cellularneural network (CNN) with five local state variables are presented. The application to a Hyper-chaossynchronization Chua's circuit (HCSCC) CNN with 1125 variables is studied. The bifurcation diagramsof the HCSCC CNN show that they are slightly different from the smoothed CNN with one or two portsand four state variables calculated earlier. The evolution of the patterns of the state variables ofthe HCSCC CNN is stimulated. Oscillatory patterns, chaotic patterns, convergent or divergentpatterns may emerge if the selected cell parameters are located in the locally active domains butnearby or in the edge of chaos domain.
文摘This paper studies chaos synchronization in the modified Chua ' s circuitwith nonlinear quadratic function x|x| using a unidirectional Linear coupling approach. A newsufficient condition is derived for chaos synchronization between the two unidirectional coupledmodified Chua ' s circuits with x x I based on the Lyapunov stability theory. A simulation exampleis given for demonstration .
文摘We introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry, especially in the frame of chaotic attractors for solving practical problems(generating hyperchaos; developing chaos based pseudo random number generator(CPRNG) and chaotic multistream PRNG; secure communication via synchronization). They can also be used in cryptography, generic algorithms in optimization, control, etc.
文摘Secure communication through chaos synchronization using small time continuous feedback is investigated. The factor K\-r>2 for guaranteeing good recovery of the information signal is determined. The simulation circuit experiment is given by PSPICE circuit simulator. Theory and experiment demonstrate that the secure communication by small time continuous feedback method does not require the system to be divided into subsystems, and has no limitation of signal to noise ratio.
文摘In this paper, a new type of chaos shift keying(CSK) modulation, called multi state CSK, is analyzed and tested. In this type of modulation combined with feedback synchronization, the data rate can be greatly increased. Laboratory test results confirm very well with theoretical analysis.
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 Major State Basic Research Development Program of China(Grant No.2012CB215202)the National Natural Science Foundation of China(Grant Nos.61104080 and 61134001)the Fundamental Research Funds for the Central Universities(Grant No.CDJZR13 175501)
文摘Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua＇s circuit.
