By the control method independent of system parameters, synchronization of two Chen chaotic systems with identical, but uncertain parameters is discussed in this article. Based on Lyapunov＇s theorem, an adaptive cont...By the control method independent of system parameters, synchronization of two Chen chaotic systems with identical, but uncertain parameters is discussed in this article. Based on Lyapunov＇s theorem, an adaptive controller and the parameters estimate update law are derived to make the solution of the error dynamical equation converge at the point E（0, 0,0） with a quick speed, that is, the states of two Chen chaotic systems can be asymptotically synchronized. Numerical simulations verify the effectiveness and the adaptivity to the variation of Chen system parameters.展开更多
The paper discusses lag synchronization of Lorenz chaotic system with three uncertain parameters. Based on adaptive technique, the lag synchronization of Lorenz chaotic system is achieved by designing a novel nonlinea...The paper discusses lag synchronization of Lorenz chaotic system with three uncertain parameters. Based on adaptive technique, the lag synchronization of Lorenz chaotic system is achieved by designing a novel nonlinear controller. Furthermore, the parameters identification is realized simultaneously. A sufficient condition is given and proved theoreticcally by Lyapunov stability theory and LaSalle’s invariance principle. Finally, the numerical simulations are provided to show the effectiveness and feasibility of the proposed method.展开更多
A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchron...A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchronization （HPS） as its special cases, Based on the adaptive technique and Lyapunov stability theory, a general method for achieving the LGS between two chaotic or hyperehaotic systems with uncertain parameters in any scaling matrix is presented. Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.展开更多
This paper addresses the adaptive synchronization for uncertain Liu system via a nonlinear input. By using a single nonlinear controller, the approach is utilized to implement the synchronization of Liu system with to...This paper addresses the adaptive synchronization for uncertain Liu system via a nonlinear input. By using a single nonlinear controller, the approach is utilized to implement the synchronization of Liu system with total parameters unknown. This method is simple and can be easily designed. What is more, it improves the existing conclusions in Ref [12]. Simulation results prove that the controller is effective and feasible in the end.展开更多
In this paper, we propose a novel approach for simultaneously identifying unknown parameters and synchronizing time-delayed complex community networks with nonidentical nodes. Based on the LaSalle＇s invariance princi...In this paper, we propose a novel approach for simultaneously identifying unknown parameters and synchronizing time-delayed complex community networks with nonidentical nodes. Based on the LaSalle＇s invariance principle, a cri- teflon is established by constructing an effective control identification scheme and adjusting automatically the adaptive coupling strength. The proposed control law is applied to a complex community network which is periodically synchro- nized with different chaotic states. Numerical simulations are conducted to demonstrate the feasibility of the proposed method.展开更多
A parameter adaptive control approach was applied to a kind of financial chaotic systems.According to Lyapunov stability theorem,synchronization of two financial chaotic systems with different certain parameters or th...A parameter adaptive control approach was applied to a kind of financial chaotic systems.According to Lyapunov stability theorem,synchronization of two financial chaotic systems with different certain parameters or the same uncertain parameters were implemented through designing proper control functions and using parameters self-adaptive control principle.The sufficient synchronization conditions of the two financial systems were obtained.Under the situation of the same uncertain parameters,the synchronization system has simpler controller and better performance.Numerical simulations show the effectiveness of the method.展开更多
Chaos synchronization of Chen chaotic system for parameters unknown isdiscussed in this paper using a scalar output. Using the concept of conditional Lyapunov exponents,the negativity of all Lyapunov exponents shows t...Chaos synchronization of Chen chaotic system for parameters unknown isdiscussed in this paper using a scalar output. Using the concept of conditional Lyapunov exponents,the negativity of all Lyapunov exponents shows the synchronization of transmitter systems withreceiver systems even though system parametes are not known to receiver systems.展开更多
The anti-synchronization between different chaotic/hyperchaotic systems with fully unknown parameters is considered in detail. Based on Lyapunov stability theory, the adaptive control schemes and parameter update rule...The anti-synchronization between different chaotic/hyperchaotic systems with fully unknown parameters is considered in detail. Based on Lyapunov stability theory, the adaptive control schemes and parameter update rules are designed in this paper. Two numerical examples show the effectiveness and feasibility of the proposed method.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
This paper proposes a simple scheme for the lag synchronization and the parameter identification of fractional order chaotic systems based on the new stability theory. The lag synchronization is achieved and the unkno...This paper proposes a simple scheme for the lag synchronization and the parameter identification of fractional order chaotic systems based on the new stability theory. The lag synchronization is achieved and the unknown parameters are identified by using the adaptive lag laws. Moreover, the scheme is analytical and is simple to implement in practice. The well-known fractional order chaotic L/i system is used to illustrate the validity of this theoretic method.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
Over the past decades, complex networks have been prosperous greatly in various fields of sciences and engineering. Much attention has been given to investigate the synchronization of complex networks in recent years....Over the past decades, complex networks have been prosperous greatly in various fields of sciences and engineering. Much attention has been given to investigate the synchronization of complex networks in recent years. However, few work has done for the networks with uncertain parameters and unknown topology. In this paper, to further reveal the dynamical mechanism in complex networks with time delays, an uncertain general complex dynamical network with delayed nodes is studied. By constructing a drive network and a suitable slave network, several novel criteria for the networks consisting of the identical nodes and different nodes have been obtained based on the adaptive feedback method. Particularly, the hypotheses and the proposed adaptive laws for network synchronization are simple and can be readily applied in practical applications. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed synchronization criteria.展开更多
This paper proposes an adaptive parameter identification method for breaking chaotic shift key communication from the transmitted signal in public channel. The sensitive dependence property of chaos on parameter misma...This paper proposes an adaptive parameter identification method for breaking chaotic shift key communication from the transmitted signal in public channel. The sensitive dependence property of chaos on parameter mismatch is used for chaos adaptive synchronization and parameter identification. An index function about the synchronization error is defined and conjugate gradient method is used to minimize the index function and to search the transmitter＇s parameter （key）. By using proposed method, secure key is recovered from transmitted signal generated by low dimensional chaos and hyper chaos switching communication. Multi-parameters can also be identified from the transmitted signal with noise.展开更多
基金the National Natural Science Foundation of Zhejiang Province （Y105320）.
文摘By the control method independent of system parameters, synchronization of two Chen chaotic systems with identical, but uncertain parameters is discussed in this article. Based on Lyapunov＇s theorem, an adaptive controller and the parameters estimate update law are derived to make the solution of the error dynamical equation converge at the point E（0, 0,0） with a quick speed, that is, the states of two Chen chaotic systems can be asymptotically synchronized. Numerical simulations verify the effectiveness and the adaptivity to the variation of Chen system parameters.
文摘The paper discusses lag synchronization of Lorenz chaotic system with three uncertain parameters. Based on adaptive technique, the lag synchronization of Lorenz chaotic system is achieved by designing a novel nonlinear controller. Furthermore, the parameters identification is realized simultaneously. A sufficient condition is given and proved theoreticcally by Lyapunov stability theory and LaSalle’s invariance principle. Finally, the numerical simulations are provided to show the effectiveness and feasibility of the proposed method.
基金the National Natural Science Foundation of China (60574045 10661006).
文摘A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchronization （HPS） as its special cases, Based on the adaptive technique and Lyapunov stability theory, a general method for achieving the LGS between two chaotic or hyperehaotic systems with uncertain parameters in any scaling matrix is presented. Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.
基金Project supported by the Educational Commission of Hubei Province of China,(Grant No 080056)
文摘This paper addresses the adaptive synchronization for uncertain Liu system via a nonlinear input. By using a single nonlinear controller, the approach is utilized to implement the synchronization of Liu system with total parameters unknown. This method is simple and can be easily designed. What is more, it improves the existing conclusions in Ref [12]. Simulation results prove that the controller is effective and feasible in the end.
基金Project supported by the Key Program of the National Natural Science of China(Grant No.11232009)the Shanghai Leading Academic Discipline Project,China(Grant No.S30106)
文摘In this paper, we propose a novel approach for simultaneously identifying unknown parameters and synchronizing time-delayed complex community networks with nonidentical nodes. Based on the LaSalle＇s invariance principle, a cri- teflon is established by constructing an effective control identification scheme and adjusting automatically the adaptive coupling strength. The proposed control law is applied to a complex community network which is periodically synchro- nized with different chaotic states. Numerical simulations are conducted to demonstrate the feasibility of the proposed method.
基金supported by Doctor Fund Item of Chongqing University of Posts and Telecommunications granted A2006-85 and Science Fund Item of Chongqing teaching committee granted KJ060506the scienceand technology research program of the municipal education committee of chongqing of granted KJ080524
文摘A parameter adaptive control approach was applied to a kind of financial chaotic systems.According to Lyapunov stability theorem,synchronization of two financial chaotic systems with different certain parameters or the same uncertain parameters were implemented through designing proper control functions and using parameters self-adaptive control principle.The sufficient synchronization conditions of the two financial systems were obtained.Under the situation of the same uncertain parameters,the synchronization system has simpler controller and better performance.Numerical simulations show the effectiveness of the method.
文摘Chaos synchronization of Chen chaotic system for parameters unknown isdiscussed in this paper using a scalar output. Using the concept of conditional Lyapunov exponents,the negativity of all Lyapunov exponents shows the synchronization of transmitter systems withreceiver systems even though system parametes are not known to receiver systems.
基金Supported by National Natural Science Foundation of China(No.60874113)
文摘The anti-synchronization between different chaotic/hyperchaotic systems with fully unknown parameters is considered in detail. Based on Lyapunov stability theory, the adaptive control schemes and parameter update rules are designed in this paper. Two numerical examples show the effectiveness and feasibility of the proposed method.
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 Natural Science Foundation of Hebei Province,China (Grant No.A2010000343)
文摘This paper proposes a simple scheme for the lag synchronization and the parameter identification of fractional order chaotic systems based on the new stability theory. The lag synchronization is achieved and the unknown parameters are identified by using the adaptive lag laws. Moreover, the scheme is analytical and is simple to implement in practice. The well-known fractional order chaotic L/i system is used to illustrate the validity of this theoretic method.
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.
基金This work was jointly supported by the National Natural Science Foundation of China under Grant No. 11047114, the Key Project of Chinese Ministry of Education under Grant No. 210141, and the Youth Project of Hubei Education Department under Grant No. Q20101609.
文摘Over the past decades, complex networks have been prosperous greatly in various fields of sciences and engineering. Much attention has been given to investigate the synchronization of complex networks in recent years. However, few work has done for the networks with uncertain parameters and unknown topology. In this paper, to further reveal the dynamical mechanism in complex networks with time delays, an uncertain general complex dynamical network with delayed nodes is studied. By constructing a drive network and a suitable slave network, several novel criteria for the networks consisting of the identical nodes and different nodes have been obtained based on the adaptive feedback method. Particularly, the hypotheses and the proposed adaptive laws for network synchronization are simple and can be readily applied in practical applications. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed synchronization criteria.
基金Project supported by the China Postdoctoral Science Foundation (Grant No 20060390318)Natural Science Foundation of Shaanxi Province (Grant No 2007F017)Fok Ying Tong Education Foundation
文摘This paper proposes an adaptive parameter identification method for breaking chaotic shift key communication from the transmitted signal in public channel. The sensitive dependence property of chaos on parameter mismatch is used for chaos adaptive synchronization and parameter identification. An index function about the synchronization error is defined and conjugate gradient method is used to minimize the index function and to search the transmitter＇s parameter （key）. By using proposed method, secure key is recovered from transmitted signal generated by low dimensional chaos and hyper chaos switching communication. Multi-parameters can also be identified from the transmitted signal with noise.
