Dynamic Behavior Analysis Of Two Kinds Of Delayed Neural Networks

In recent years, neural networks have been developed rapidly and applied widely in many fields including signal processing, decision aids, pattern recognition, image processing, combinatorial optimization, parallel computing, automatic control and so on. It is well known that the stability and convergence of neural network are the premise and foundation for its application, so the analysis of the dynamic behaviors for neural network becomes a research focus. In addition, delay would arise in the process of hardware implementation and application of neural network, which could influence the dynamic behavior of neural networks and make systems oscillate or unstable. For a time-varying delay, the dynamic behavior of system will become more complex. So, it is very necessary to study neural networks with time-varying delay.In this thesis, we mainly discuss two kinds of neural networks:single neuron neutral type system with time-varying delays and recurrent neural networks with time-varying delay, and analyze their dynamic behaviors. By using linear matrix in-equalities and constructing appropriate Lyapunov-Krasovskii functional containing the information of activation function and delay, the stability criterions with less conservatism for them are given respectively.In chapter 1, the history of neural networks is firstly reviewed. Then the progress of neural networks with time delay is introduced. Next, some prelimi-naries are listed, which include some essential definitions, theorems, inequalities and lemmas. The main work is summarized at the end of this chapter.In chapter 2, we investigate the exponential stability of single neuron neutral type system with time-varying delays and non-monotonic and unbounded activa-tion function. By constructing appropriate Lyapunov-Krasovskii functional and using theory on differential equations, a sufficient condition is provided to ensure exponential stability of underlying system. This condition can be easily verified by MATLAB since it is a linear matrix inequality. The obtained result generalizes some existing results and its correctness is supported by numerical examples.In chapter 3, we analyze the global asymptotical stability of neural networks with time-varying delay. An appropriate Lyapunov-Krasovskii functional containing triple integral terms is first constructed, and its derivative is then estimated by using more refined integral inequality. Finally, a delay-dependent stability criteria for global asymptotic stability for this network is provided by using delay partitioning method. Compared with the existing results, the given criteria is less conservative and easy to verify. Numerical examples are also provided to illustrate the feasibility of the proposed method and support the obtained results.