Based on the stability theory of linear time-varying continuous system, this paper investigates the synchronization of two linear bidirectionally-coupled systems. Sufficient conditions for asymptotic synchronization a...Based on the stability theory of linear time-varying continuous system, this paper investigates the synchronization of two linear bidirectionally-coupled systems. Sufficient conditions for asymptotic synchronization are obtained for general chaotic system with bidirectional coupling via linear error feedback. Since the trajectory of chaotic system is continuous and bounded, one can choose suitable coupled pararneters to satisfy the proposed criterion. The criterion can also be applied to the global synchronization for chaotic systems with linear unidirectional coupling. The chaotic Chen system and the generalized Lorenz-like system are taken as examples, the simulations verify the effectiveness of the proposed method.展开更多
In this paper we study the chaos synchronization and anti-synchronization problems between two hyper-chaotic systems with bidirectional coupling,and present synchronization and anti-synchronization methods of chaotic ...In this paper we study the chaos synchronization and anti-synchronization problems between two hyper-chaotic systems with bidirectional coupling,and present synchronization and anti-synchronization methods of chaotic systems,based on timedelayed feedback.Coupling coefficients between the drive and response systems are different,which are supposed to be nonlinearly coupled.Based on the nonlinear control theory,the synchronization and anti-synchronization between two different time-delay hyper-chaotic systems are investigated.The condition of synchronization is derived according to the error dynamical systems.Numerical simulations show the effectiveness and feasibility of the proposed synchronous conditions.展开更多
Outer synchronization between two different fractional-order general complex dynamical networks is investigated in this paper. Based on the stability theory of the fractional-order system, the sufficient criteria for ...Outer synchronization between two different fractional-order general complex dynamical networks is investigated in this paper. Based on the stability theory of the fractional-order system, the sufficient criteria for outer synchronization are derived analytically by applying the nonlinear control and the bidirectional coupling methods. The proposed synchronization method is applicable to almost all kinds of coupled fractional-order general complex dynamical networks. Neither a symmetric nor irreducible coupling configuration matrix is required. In addition, no constraint is imposed on the inner-coupling matrix. Numerical examples are also provided to demonstrate the validity of the presented synchronization scheme. Numeric evidence shows that both the feedback strength k and the fractional order a can be chosen appropriately to adjust the synchronization effect effectively.展开更多
In this paper, two different ring networks with unidirectional couplings and with bidirectional couplings were discussed by theoretical analysis. It was found that the effects on synchronizing ability of the two diffe...In this paper, two different ring networks with unidirectional couplings and with bidirectional couplings were discussed by theoretical analysis. It was found that the effects on synchronizing ability of the two different structures by cutting a link are completely opposite. The synchronizing ability will decrease if the change is from bidirectional ring to bidirectional chain. Moreover, the change on synchronizing ability will be four times if the number of N is large enough. However, it will increase obviously from unidirectional ring to unidirectional chain. It will be N^2/（π^2） times if the number of N is large enough. The numerical simulations confirm the conclusion in quality. This paper also discusses the effects on synchronization by adding one link with different length d to these two different structures. It can be seen that the effects are different. Theoretical results are accordant to numerical simulations. Synchronization is an essential physics problem. These results proposed in this paper have some important reference meanings on the real world networks, such as the bioecological system networks, the designing of the circuit, etc.展开更多
本文研究了具有时间延迟的异结构不确定网络之间的外同步问题.基于Lyapunov稳定性理论,采用双向耦合自适应方法实现了两个结构互异的复杂网络之间的外同步.并且,网络的拓扑结构以及耦合强度也被同时确定.在数值模拟中,选取Van der Pol...本文研究了具有时间延迟的异结构不确定网络之间的外同步问题.基于Lyapunov稳定性理论,采用双向耦合自适应方法实现了两个结构互异的复杂网络之间的外同步.并且,网络的拓扑结构以及耦合强度也被同时确定.在数值模拟中,选取Van der Pol系统和Duffing系统作为网络节点进行仿真模拟,验证其理论结果的有效性.展开更多
基金This work was supported bythe National Natural Science Foundation (No .60174005) Natural Science Foundation of Jiangsu Province (No .BK2001054) .
文摘Based on the stability theory of linear time-varying continuous system, this paper investigates the synchronization of two linear bidirectionally-coupled systems. Sufficient conditions for asymptotic synchronization are obtained for general chaotic system with bidirectional coupling via linear error feedback. Since the trajectory of chaotic system is continuous and bounded, one can choose suitable coupled pararneters to satisfy the proposed criterion. The criterion can also be applied to the global synchronization for chaotic systems with linear unidirectional coupling. The chaotic Chen system and the generalized Lorenz-like system are taken as examples, the simulations verify the effectiveness of the proposed method.
基金Supported by Scientific and Technological Research Project of The Education Department Henan Province(12B110012)
文摘In this paper we study the chaos synchronization and anti-synchronization problems between two hyper-chaotic systems with bidirectional coupling,and present synchronization and anti-synchronization methods of chaotic systems,based on timedelayed feedback.Coupling coefficients between the drive and response systems are different,which are supposed to be nonlinearly coupled.Based on the nonlinear control theory,the synchronization and anti-synchronization between two different time-delay hyper-chaotic systems are investigated.The condition of synchronization is derived according to the error dynamical systems.Numerical simulations show the effectiveness and feasibility of the proposed synchronous conditions.
基金supported by the National Natural Science Foundation of China (Grant No. 60873133)the National High Technology Research and Development Program of China (Grant No. 2007AA01Z478)
文摘Outer synchronization between two different fractional-order general complex dynamical networks is investigated in this paper. Based on the stability theory of the fractional-order system, the sufficient criteria for outer synchronization are derived analytically by applying the nonlinear control and the bidirectional coupling methods. The proposed synchronization method is applicable to almost all kinds of coupled fractional-order general complex dynamical networks. Neither a symmetric nor irreducible coupling configuration matrix is required. In addition, no constraint is imposed on the inner-coupling matrix. Numerical examples are also provided to demonstrate the validity of the presented synchronization scheme. Numeric evidence shows that both the feedback strength k and the fractional order a can be chosen appropriately to adjust the synchronization effect effectively.
基金the National Basic Research 973 Program of China (Grant No. 2006CB708302)the National Natural Science Foundation of China (Grant Nos. 60574045 and 90604005)
文摘In this paper, two different ring networks with unidirectional couplings and with bidirectional couplings were discussed by theoretical analysis. It was found that the effects on synchronizing ability of the two different structures by cutting a link are completely opposite. The synchronizing ability will decrease if the change is from bidirectional ring to bidirectional chain. Moreover, the change on synchronizing ability will be four times if the number of N is large enough. However, it will increase obviously from unidirectional ring to unidirectional chain. It will be N^2/（π^2） times if the number of N is large enough. The numerical simulations confirm the conclusion in quality. This paper also discusses the effects on synchronization by adding one link with different length d to these two different structures. It can be seen that the effects are different. Theoretical results are accordant to numerical simulations. Synchronization is an essential physics problem. These results proposed in this paper have some important reference meanings on the real world networks, such as the bioecological system networks, the designing of the circuit, etc.
文摘本文研究了具有时间延迟的异结构不确定网络之间的外同步问题.基于Lyapunov稳定性理论,采用双向耦合自适应方法实现了两个结构互异的复杂网络之间的外同步.并且,网络的拓扑结构以及耦合强度也被同时确定.在数值模拟中,选取Van der Pol系统和Duffing系统作为网络节点进行仿真模拟,验证其理论结果的有效性.
