In this paper is investigated the generalized projective synchronization of a class of chaotic (or hyperchaotic) systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive...In this paper is investigated the generalized projective synchronization of a class of chaotic (or hyperchaotic) systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic (hyperchaotic) systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.展开更多
Projective synchronization and generalized projective synchronization have recently been observed in the coupled chaotic systems. In this paper, a new synchronization, called "generalized projective synchronization"...Projective synchronization and generalized projective synchronization have recently been observed in the coupled chaotic systems. In this paper, a new synchronization, called "generalized projective synchronization", is reported in the chaotic Lorenz system and the chaotic Chen one.展开更多
Based on symbolic computation system Maple and Lyapunov stability theory,an active control method isused to projectively synchronize two different chaotic systems—Lorenz-Chen-Lü system(LCL)and Rssler system,whic...Based on symbolic computation system Maple and Lyapunov stability theory,an active control method isused to projectively synchronize two different chaotic systems—Lorenz-Chen-Lü system(LCL)and Rssler system,which belong to different dynamic systems.In this paper,we achieve generalized projective synchronization between thetwo different chaotic systems by directing the scaling factor onto the desired value arbitrarily.To illustrate our result,numerical simulations are used to perform the process of the synchronization and successfully put the orbits of drivesystem(LCL)and orbits of the response system(Rssler system)in the same plot for understanding intuitively.展开更多
Based on the stability theory of the fractional order system, the dynamic behaviours of a new fractional order system are investigated theoretically. The lowest order we found to have chaos in the new three-dimensiona...Based on the stability theory of the fractional order system, the dynamic behaviours of a new fractional order system are investigated theoretically. The lowest order we found to have chaos in the new three-dimensional system is 2.46, and the period routes to chaos in the new fractional order system are also found. The effectiveness of our analysis results is further verified by numerical simulations and positive largest Lyapunov exponent. Furthermore, a nonlinear feedback controller is designed to achieve the generalized projective synchronization of the fractional order chaotic system, and its validity is proved by Laplace transformation theory.展开更多
This paper presents a general method of the generalized projective synchronization and the parameter identification between two different chaotic systems with unknown parameters. This approach is based on Lyapunov sta...This paper presents a general method of the generalized projective synchronization and the parameter identification between two different chaotic systems with unknown parameters. This approach is based on Lyapunov stability theory, and employs a combination of feedback control and adaptive control. With this method one can achieve the generalized projective synchronization and realize the parameter identifications between almost all chaotic (hyperchaotic) systems with unknown parameters. Numerical simulations results are presented to demonstrate the effectiveness of the method.展开更多
This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 ...This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 〈 q 〈 1 is obtained based on the stability theory of the fractional-order system. The control method which combines active control with pinning control is then suggested to obtain the controllers. Furthermore, the adaptive strategy is applied to tune the control gains and coupling strength. Corresponding numerical simulations are performed to verify and illustrate the theoretical results.展开更多
Based on the improved state observer and the pole placement technique, by adding a constant which extends the scope of use of the original system, a new design method of generalized projective synchronization is propo...Based on the improved state observer and the pole placement technique, by adding a constant which extends the scope of use of the original system, a new design method of generalized projective synchronization is proposed. With this method, by changing the projective synchronization scale factor, one can achieve not only complete synchronization, but also anti-synchronization, as well as arbitrary percentage of projective synchronization, so that the system may attain arbitrary synchronization in a relatively short period of time, which makes this study more meaningful. By numerical simulation, and choosing appropriate scale factor, the results of repeated experiments verify that this method is highly effective and satisfactory. Finally, based on this method and the relevant feedback concept, a novel secure communication project is designed. Numerical simulation verifies that this secure communication project is very valid, and moreover, the experimental result has been greatly improved in decryption time.展开更多
Based on the Chen chaotic system, this paper constructs a new three-dimensional chaotic system with higher order nonlinear term and studies the basic dynamic behaviours of the system. The modified generalized projecti...Based on the Chen chaotic system, this paper constructs a new three-dimensional chaotic system with higher order nonlinear term and studies the basic dynamic behaviours of the system. The modified generalized projective synchronization has been observed in the coupled new three-dimensional chaotic system with unknown parameters. Furthermore, based on Lyapunov stability theory, it obtains the control laws and adaptive laws of parameters to make modified generalized projective synchronization of the coupled new three-dimensional chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.展开更多
In this paper, the chaotic generalized projective synchronization of a controlled, noised gyro with an expected gyro is investigated by a simple control law. Based on the theory of discontinuous dynamical systems, the...In this paper, the chaotic generalized projective synchronization of a controlled, noised gyro with an expected gyro is investigated by a simple control law. Based on the theory of discontinuous dynamical systems, the necessary and sufficient conditions for such a synchronization are achieved. From such conditions, non-synchronization, partial and full synchronizations between the two coupled gyros are discussed. The switching scenarios between desynchronized and synchronized states of the two dynamical systems are shown. Numerical simulations are illustrated to verify the effectiveness of this method.展开更多
An adaptive fuzzy sliding mode strategy is developed for the generalized projective synchronization of a fractional- order chaotic system, where the slave system is not necessarily known in advance. Based on the desig...An adaptive fuzzy sliding mode strategy is developed for the generalized projective synchronization of a fractional- order chaotic system, where the slave system is not necessarily known in advance. Based on the designed adaptive update laws and the linear feedback method, the adaptive fuzzy sliding controllers are proposed via the fuzzy design, and the strength of the designed controllers can he adaptively adjusted according to the external disturbances. Based on the Lya- punov stability theorem, the stability and the robustness of the controlled system are proved theoretically. Numerical simu- lations further support the theoretical results of the paper and demonstrate the efficiency of the proposed method. Moreover, it is revealed that the proposed method allows us to manipulate arbitrarily the response dynamics of the slave system by adjusting the desired scaling factor λi and the desired translating factor ηi, which may be used in a channel-independent chaotic secure communication.展开更多
In this paper,some basic properties of a new four-dimensional(4 D)continuous autonomous chaotic system,in which each equation contains a cubic cross-product term,are further analyzed.The new system has 9 equilibria di...In this paper,some basic properties of a new four-dimensional(4 D)continuous autonomous chaotic system,in which each equation contains a cubic cross-product term,are further analyzed.The new system has 9 equilibria displaying graceful symmetry with respect to the origin and coordinate planes,and the stability of them are discussed.Then detailed bifurcation analysis is given to demonstrate the evolution processes of the system.Numerical simulations show that the system evolves chaotic motions through period-doubling bifurcation or intermittence chaos while the system parameters vary.We design a new scheme of generalized projective synchronization,so-called unified generalized projective synchronization,whose response signal synchronizes with the linear combination of drive signal.The design has the advantages of containing complete synchronization,anti-synchronization and disorder synchronization over the usual generalized projective synchronization,such that it can provide greater security in secure communication.Based on Lyapunov stability theorem,some sufficient conditions for the new synchronization are inferred.Numerical simulations demonstrate the effectiveness and feasibility of the method by employing the four-wing chaotic system.展开更多
The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on Lyapunov stability theory...The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on Lyapunov stability theory and Barbalat's lemma, generalized matrix projective lag synchronization criteria are derived by using the adaptive control method. Furthermore, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. In addition, numerical simulation results are presented to illustrate the effectiveness of this method, showing that the synchronization speed is sensitively influenced by the adaptive law strength, the network size, and the network topological structure.展开更多
A novel fractional-order hyperchaotic complex system is proposed by introducing the Caputo fractional-order derivative operator and a constant term to the complex simplified Lorenz system. The proposed system has diff...A novel fractional-order hyperchaotic complex system is proposed by introducing the Caputo fractional-order derivative operator and a constant term to the complex simplified Lorenz system. The proposed system has different numbers of equilibria for different ranges of parameters. The dynamics of the proposed system is investigated by means of phase portraits, Lyapunov exponents, bifurcation diagrams, and basins of attraction. The results show abundant dynamical characteristics. Particularly, the phenomena of extreme multistability as well as hidden attractors are discovered. In addition, the complex generalized projective synchronization is implemented between two fractional-order hyperchaotic complex systems with different fractional orders. Based on the fractional Lyapunov stability theorem, the synchronization controllers are designed, and the theoretical results are verified and demonstrated by numerical simulations. It lays the foundation for practical applications of the proposed system.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No 60574045) and partly by Foundation of Guangxi Department of Education, China (Grant No (2006)26-118).
文摘In this paper is investigated the generalized projective synchronization of a class of chaotic (or hyperchaotic) systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic (hyperchaotic) systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.
基金Project supported by Tianyuan Foundation of China ( Grant No. A0324651), and Natural Science Foundation of Hunaa Province of China (Grant No. 03JJY3014)
文摘Projective synchronization and generalized projective synchronization have recently been observed in the coupled chaotic systems. In this paper, a new synchronization, called "generalized projective synchronization", is reported in the chaotic Lorenz system and the chaotic Chen one.
基金the Natural Science Foundation of Zhejiang Province of China under Grant No.Y604056the Doctoral Foundation of Ningbo City under Grant No.2005A610030
文摘Based on symbolic computation system Maple and Lyapunov stability theory,an active control method isused to projectively synchronize two different chaotic systems—Lorenz-Chen-Lü system(LCL)and Rssler system,which belong to different dynamic systems.In this paper,we achieve generalized projective synchronization between thetwo different chaotic systems by directing the scaling factor onto the desired value arbitrarily.To illustrate our result,numerical simulations are used to perform the process of the synchronization and successfully put the orbits of drivesystem(LCL)and orbits of the response system(Rssler system)in the same plot for understanding intuitively.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60573172 and 60973152)the Doctoral Program Foundation of Institution of Higher Education of China (Grant No. 20070141014)the Natural Science Foundation of Liaoning Province,China (Grant No. 20082165)
文摘Based on the stability theory of the fractional order system, the dynamic behaviours of a new fractional order system are investigated theoretically. The lowest order we found to have chaos in the new three-dimensional system is 2.46, and the period routes to chaos in the new fractional order system are also found. The effectiveness of our analysis results is further verified by numerical simulations and positive largest Lyapunov exponent. Furthermore, a nonlinear feedback controller is designed to achieve the generalized projective synchronization of the fractional order chaotic system, and its validity is proved by Laplace transformation theory.
基金Project supported by the Natural Science Foundation of Hebei Province, China (Grant No A2006000128)
文摘This paper presents a general method of the generalized projective synchronization and the parameter identification between two different chaotic systems with unknown parameters. This approach is based on Lyapunov stability theory, and employs a combination of feedback control and adaptive control. With this method one can achieve the generalized projective synchronization and realize the parameter identifications between almost all chaotic (hyperchaotic) systems with unknown parameters. Numerical simulations results are presented to demonstrate the effectiveness of the method.
文摘This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 〈 q 〈 1 is obtained based on the stability theory of the fractional-order system. The control method which combines active control with pinning control is then suggested to obtain the controllers. Furthermore, the adaptive strategy is applied to tune the control gains and coupling strength. Corresponding numerical simulations are performed to verify and illustrate the theoretical results.
基金Project supported by the China Postdoctoral Science Foundation (Grant No. 20080431142)
文摘Based on the improved state observer and the pole placement technique, by adding a constant which extends the scope of use of the original system, a new design method of generalized projective synchronization is proposed. With this method, by changing the projective synchronization scale factor, one can achieve not only complete synchronization, but also anti-synchronization, as well as arbitrary percentage of projective synchronization, so that the system may attain arbitrary synchronization in a relatively short period of time, which makes this study more meaningful. By numerical simulation, and choosing appropriate scale factor, the results of repeated experiments verify that this method is highly effective and satisfactory. Finally, based on this method and the relevant feedback concept, a novel secure communication project is designed. Numerical simulation verifies that this secure communication project is very valid, and moreover, the experimental result has been greatly improved in decryption time.
文摘Based on the Chen chaotic system, this paper constructs a new three-dimensional chaotic system with higher order nonlinear term and studies the basic dynamic behaviours of the system. The modified generalized projective synchronization has been observed in the coupled new three-dimensional chaotic system with unknown parameters. Furthermore, based on Lyapunov stability theory, it obtains the control laws and adaptive laws of parameters to make modified generalized projective synchronization of the coupled new three-dimensional chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.
基金supported by the National Natural Science Foundation of China (Grant No. 51075275)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 08kJB510006)
文摘In this paper, the chaotic generalized projective synchronization of a controlled, noised gyro with an expected gyro is investigated by a simple control law. Based on the theory of discontinuous dynamical systems, the necessary and sufficient conditions for such a synchronization are achieved. From such conditions, non-synchronization, partial and full synchronizations between the two coupled gyros are discussed. The switching scenarios between desynchronized and synchronized states of the two dynamical systems are shown. Numerical simulations are illustrated to verify the effectiveness of this method.
基金Project supported by the Research Foundation of Education Bureau of Hebei Province,China(Grant No.QN2014096)
文摘An adaptive fuzzy sliding mode strategy is developed for the generalized projective synchronization of a fractional- order chaotic system, where the slave system is not necessarily known in advance. Based on the designed adaptive update laws and the linear feedback method, the adaptive fuzzy sliding controllers are proposed via the fuzzy design, and the strength of the designed controllers can he adaptively adjusted according to the external disturbances. Based on the Lya- punov stability theorem, the stability and the robustness of the controlled system are proved theoretically. Numerical simu- lations further support the theoretical results of the paper and demonstrate the efficiency of the proposed method. Moreover, it is revealed that the proposed method allows us to manipulate arbitrarily the response dynamics of the slave system by adjusting the desired scaling factor λi and the desired translating factor ηi, which may be used in a channel-independent chaotic secure communication.
基金Supported by the National Natural Science Foundation of China(61863022)the Natural Science Foundation of Gansu Province(17JR5RA096)。
文摘In this paper,some basic properties of a new four-dimensional(4 D)continuous autonomous chaotic system,in which each equation contains a cubic cross-product term,are further analyzed.The new system has 9 equilibria displaying graceful symmetry with respect to the origin and coordinate planes,and the stability of them are discussed.Then detailed bifurcation analysis is given to demonstrate the evolution processes of the system.Numerical simulations show that the system evolves chaotic motions through period-doubling bifurcation or intermittence chaos while the system parameters vary.We design a new scheme of generalized projective synchronization,so-called unified generalized projective synchronization,whose response signal synchronizes with the linear combination of drive signal.The design has the advantages of containing complete synchronization,anti-synchronization and disorder synchronization over the usual generalized projective synchronization,such that it can provide greater security in secure communication.Based on Lyapunov stability theorem,some sufficient conditions for the new synchronization are inferred.Numerical simulations demonstrate the effectiveness and feasibility of the method by employing the four-wing chaotic system.
文摘The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on Lyapunov stability theory and Barbalat's lemma, generalized matrix projective lag synchronization criteria are derived by using the adaptive control method. Furthermore, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. In addition, numerical simulation results are presented to illustrate the effectiveness of this method, showing that the synchronization speed is sensitively influenced by the adaptive law strength, the network size, and the network topological structure.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 62071496, 61901530, and 62061008)the Innovation Project of Graduate of Central South University (Grant No. 2022zzts0681)。
文摘A novel fractional-order hyperchaotic complex system is proposed by introducing the Caputo fractional-order derivative operator and a constant term to the complex simplified Lorenz system. The proposed system has different numbers of equilibria for different ranges of parameters. The dynamics of the proposed system is investigated by means of phase portraits, Lyapunov exponents, bifurcation diagrams, and basins of attraction. The results show abundant dynamical characteristics. Particularly, the phenomena of extreme multistability as well as hidden attractors are discovered. In addition, the complex generalized projective synchronization is implemented between two fractional-order hyperchaotic complex systems with different fractional orders. Based on the fractional Lyapunov stability theorem, the synchronization controllers are designed, and the theoretical results are verified and demonstrated by numerical simulations. It lays the foundation for practical applications of the proposed system.