Chaos Control And Synchronization Of Complex Hinmarsh-Rose Neural Network With Nonlinear Time Delay Coupling Function

In recent years, there is a breakthrough development in the area of controlling and synchronization of chaos. The research of theoretical and experimental application is promoted vigorously. The chaos control and synchronization has been widely researched in the system of physics, chemistry and biology, especially it also played an important role in biological and artificial neural networks. With the development of chaos control and synchronization, the chaos control and synchronization of neural networks has attracted much attention. Especially for neural networks which are conducted by Hindmarsh-Rose neuron. Currently, the research of the complex network has been developing vigorously at home and abroad. It has shown promising development and application prospect.Hindmarsh-Rose neurons show abundant dynamics models including chaos and cycle. Dhamala and his co-workers uncovered a phenomenon of enhancement of neural synchrony by high time-delay and low gain factor. Yu proposed a method by using a special nonlinear-coupled term which is constructed by suitable separation between linear and nonlinear terms of the chaotic system. This method is used to discuss the synchronization of two symmetrical nonlinear-coupled chaotic systems. The stability of the synchronous state is examined by the stability criterion of linear systems and the conditional Lyapunov exponent.Based on the research of Dhamala and Yu, first we use the nonlinear time-delay feedback method to study the chaotic control of single H-R neuron. Then nonlinear time-delay coupling function is added between neurons in the neural networks to research the chaos control and synchronization of Hindmarsh-Rose neurons. The neural networks we studied in this paper including different kinds of all-to-all connection network; nearest neighbor network; star connected network, and complex neural networks composed by two subnetworks. The coupling strength and the time delay are taken as the controlling parameters. Choose of delay is un-dependent and doesn't rely on the period of unstable periodic orbits embedded within chaotic attractor. The chaotic burst orbit will be controlled onto the certain type of periodic patterns of inter-spike interval automatically.