Study On Stability Of Stochastic Delayed Neural Networks

The neural network, as an important large-scale complex system, exhibits rich and colorful dynamical behaviors. In recent twenty years, due to its important and potential applications in solving associative memories, optimizing solvers, signal processing, pattern recognition and so on, the dynamics of delayed neural networks have been investigated intensively. It is a very important to ensure the stability of neural network and its learning process. In order to analyze and apply it easily, the transmission delays are ignored in modeling of most systems. But it is demonstrated by theories and practices that time delay is unavoidable. In biological neural systems, synaptic transmission is a noisy process brought on by random fluctuations from the release of neurotransmitters and other probabilistic causes. In addition to delay and random noise in the neural network applications and design, system modeling must take into account some of the inevitable parameter uncertainty, these uncertainties mainly due to system modeling when the model simplification, parameter fluctuations and data errors. So, time delays, parameter uncertainty and stochastic disturbances may affect the stability of the system, even lead to instability, oscillation or chaos phenomena. Recently, the stability of delayed stochastic neural networks has attracted a large number of researchers, and a series of significant results have been achieved.This dissertation focuses on the asymptotical and robust stability analysis for several delayed stochastic neural networks, including delay-range-dependent stability of uncertain stochastic neural networks with time-varying delays; stability of uncertain stochastic neural networks with interval time-varying delay; stability of uncertain stochastic neural networks with distributed and interval time-varying delays; stability of uncertain stochastic BAM neural networks with interval time-varying delays; stability of stochastic neutral-type neural networks with time-varying delays. The main contributions and originality contained in this dissertation can be summarized as follows:â‘ Delay-range-dependent robust stability for uncertain stochastic neural networks with time-varying delaysThe delay-range-dependent robust stability problem for uncertain stochastic neural networks with interval time-varying delays is investigated. Some new delay-range-dependent and delay-derivative-dependent criteria are presented. Since there are some information about the derivative of the time-vary delay function in the delay-derivative-dependent criteria, the presented criteria are less conservative than delay-derivative-independent criteria.â‘¡Mean square stability of uncertain stochastic neural networks with distributed and interval time-varying delaysAs variation of the size and length of the neurons, transmission line design complexity and the limitations of artificial neural networks, the time delays is often the form of a continuous distributed delays in the signal transmission process. Thus, neural network with distributed time-varying delays are more close to practical application. We investigate the robust asymptotic stability analysis problem for stochastic uncertain neural networks with distributed and interval time-varying delays. The presented criteria remove two constraints: the derivative of time-varying delay must be less than 1 and the lower bound of time-varying delay must be equal to 0. The criteria are applicable to both fast and slow time-varying delays. So, they can widen the application range.â‘¢Global asymptotic stability analysis of stochastic neutral-type neural networks with time-varying delaysThe existence of time delays in most delayed neural networks models indicates that time delays are dependent on the past state. In fact, many practical delay systems can be modeled as differential systems of neutral type, whose differential expression concludes not only the derivative term of the current state but also concludes the derivative term of the past state. It is natural and important that systems should contain some information about the derivative of the past state to further describe and model the dynamics for such complex neural reactions. We further study the asymptotic stability of the delayed stochastic neutral-type neural networks with time-varying delays. Compared with the existing stability results of neutral-type neural networks, the activation function of neural networks studied in this chapter has a more general form.