Time Delay-the Chaotic Synchronization And Control Of Neural Networks

In the last three decades, the synchrony-and-controlling of neuralnetworks has attracted much attention in particular. Controlling andsynchronization of chaos has been widely researched in the system ofastronomy, secure communication, chemistry, physiology and so on. Theresearch of theoretical and experimental application is promotedvigorously. Currently, the research of the complex network has beendeveloping vigorously at home and abroad. It has shown promisingdevelopment and application prospect, mature theoretical system andpractical way of chaos controlling and synchronization will occupy a veryimportant position in the research activities of the future of mankind.HindmarSh-Rose(H-R) neurons show abundant dynamics modelsincluding chaos and cycle. Dhamala and his co-workers uncovered aPhenomenon of enhancement of neural synchrony by high time-delay andlower factors. Yu and her co-workers suggested a new approach forconstructing chaotically synchronizing systems by a suitable separation ofsystems is proposed. The method is based on the stability criterion oflinear systems (SC method), and the synchronization of constructedsystems is ensured by that all eigenvalues of the Jacobian matrix havenegative real parts.Based on the research of Yu, the SC method and time delay feedbackmethod are applied to control the neural networks. Firstly, we define thedifferent coupling coefficient matrixes of these two controlling methods.Then by using the coupling coefficient matrix we build the neuralnetworks we need, including fully connected network which isconstructed by4H-R neurons, and4kinds of complex networks whichare constructed by12neurons. At last, by using SC method and linear time delay feedback method, through numerical simulation, observing thecoupling strength and the time delay how to affects the chaossynchronization process and neuronal dynamics behavior, whilecomparing the difference between network synchronization process andneurons dynamic behavior which caused by different types ofconnections.