Circuitry implementation of a novel four-dimensional nonautonomous hyperchaotic Liu system and its experimental studies on synchronization control

Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperchaotic Liu system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyperchaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the two new systems are studied, respectively. Furthermore, the synchronizing circuits of the nonautonomous hyperchaotic Liu system are designed via the synchronization control method of single variable coupling feedback. Finally, the hardware circuits are implemented, and the corresponding waves of chaos are observed by an oscillograph.     

Adaptive synchronization in an array of asymmetric coupled neural networks

This paper investigates the global synchronization in an array of linearly coupled neural networks with constant and delayed coupling. By a simple combination of adaptive control and linear feedback with the updated laws, some sufficient conditions are derived for global synchronization of the coupled neural networks. The coupling configuration matrix is assumed to be asymmetric, which is more coincident with the realistic network. It is shown that the approaches developed here extend and improve the earlier works. Finally, numerical simulations are presented to demonstrate the effectiveness of the theoretical results.     

Global Synchronization of Directed Networks with Fast Switching Topologies

Global synchronization of a class of directed dynamical networks with switching topologies is investigated. It is found that if there is a directed spanning tree in the fixed time-average of network topology and the time-average is achieved sufficiently fast, then the network will reach global synchronization for sufficiently large coupling strength.     

Synchronization in Triangled Complex Networks

Using a tunable clustering coefficient model without changing the degree distribution, we investigate the effect of clustering coefficient on synchronization of networks with both unweighted and weighted couplings. For several typical categories of complex networks, the more triangles are in the networks, the worse the synchronizability of the networks is.     

Anti-control and Generalized Synchronization of Chaos for a Kind of n-Dimensional Linear Differential System

This paper introduces the finding of some chaotic attractors in a kind of n-dimensional autonomous hybrid system, which is realized via applying some discontinuous state feedback to a kind of n linear differential system. And a constructive theorem is proposed for generalized synchronization related to the above chaotic hybrid systems. Examples are presented for illustrating the methods.     

Bidirectional Partial Generalized Synchronization in Chaotic and Hyperchaotic Systems via a New Scheme

In this paper, a bidirectional partial generalized (lag, complete, and anticipated) synchronization of a class of continuous-time systems is defined. Then based on the active control idea, a new systematic and concrete scheme is developed to achieve bidirectional partial generalized (lag, complete, and anticipated) synchronization between two chaotic systems or between chaotic and hyperchaotic systems. With the help of symbolic-numerical computation, we choose the modified Chua system, Lorenz system, and the hyperchaotic Tamasevicius-Namajunas-Cenys system to illustrate the proposed scheme. Numerical simulations are used to verify the effectiveness of the proposed scheme. It is interesting that partial chaos synchronization not only can take place between two chaotic systems, but also can take place between chaotic and hyperchaotic systems. The proposed scheme can also be extended to research bidirectional partial generalized (lag, complete, and anticipated) synchronization between other dynamical systems.     

Alternate Phase Synchronization in Coupled Chaotic Oscillators

Phase locking dynamics in coupled chaotic oscillators is investigated.For chaotic systems with a poorly coherent phase variable,the imperfect phase locking can be observed befor the onset of a complete phase synchronization.The temporal alternations among n:n phase lockings are found,which originate from an overlap of m:n Arnold tongues.     

Global adaptive synchronization of chaotic systems with uncertain parameters

We propose a novel adaptive synchronization method for a class of nonlinear chaotic systems with uncertain parameters.Using the chaos control method,we derive a synchronizer,which can make the states of the driven system globally track the states of the drive system asymptotically.The advantage of our method is that our problem sctting is more general than those that already exist,and the synchronizer is simply constructed by an analytic formula,without knowledge in advance of the unknown bounds of the uncertain parameters.A computer simulation example is given to validate the proposed approach.     

Global synchronization of Chua＇s chaotic delay network by using linear matrix inequality

Global synchronization of Chua‘s chaotic dynamical networks with coupling delays is investigated in this paper.Unlike other approaches, where only local results were obtained, the network is found to be not linearized in this paper.Insteat, the global synchronization is obtained by using the linear matrix inequality theory. Moreover, some quite simple linear-state-error feedback controllers for global synchronization are derived, which can be easily constructed based on the minimum eigenvalue of the coupling matrix. A simulation of Chua‘s chaotic network with global coupling delays in nodes is finally given, which is used to verify the theoretical results of the proposed global synchron izationscheme.     

基于间歇性参数自适应控制的混沌同步

提出了在两个不同参数混沌系统的同步中基于间歇性参数自适应的控制方法.在选择合适的间歇反馈周期N和反馈系数r的情况下,可以获得满意的同步结果.以logistic映射为例进行了计算机模拟.结果表明:适当选取反馈系数r,可以以很小的控制代价实现预定的同步目的. 关键词： 混沌同步 间歇控制 自适应控制