Stochastic Disturbance Analysis On Species Models And Static Neural Network Models

Species dynamics is a subject that studies population ecology by using the dynamics methods. it investigates mainly the evolutive law on amount and structure of Species. it is widely applied in exploiture and administration of biology resource, population forecast, economics and so on. The mathematical models become more and more complicated. While most of the results about species dynamics are confined to deterministic models, few about stochastic models. In this paper, the dynamical behavior of stochastic cooperative models and competitive models is studied. Some different conclusions from the deterministic models are obtained.Artificial neural network is a very active research area in these years, it is applied in automatic-control systems,pattern recognition,image processing,optimization,signal processing,sensing technology robot,biomedical engineering and so on . Along with the genetic algorithm and the ant colony optimization's appearance, neural networks can realize stronger associative memory function. Through establishing simple movement rules to each neuron complex behavior can be realized. This causes the application prospect of neural networks to be broader. Therefore the research on neural networks is very valuable. Considering from the bionics angle, when our brains handle the event, we possibly draw different conclusions to the identical matter under different conditions. Even in the completely same situation we may have different conclusions. Therefore when our brains process information, the output result possibly will not be definite but will conform to some kind of probability distribution. This will be one kind of random phenomenon. Therefore the neural network models considering stochastic affects should be finer models. Moreover, cerebrum's each neuron needs to cooperate mutually the processing matter. Time is required when information transmitting among neurons. Therefore we must consider the influence of time delay. Now, the research on stochastic delay neural networks just started, massive work need people to do. This paper will conduct the simple qualitative investigation to the stochastic delay neural network, stability, robustness and the influence of stochastic disturbance are placed with emphasis.This article arranges as follows: The first chapter is an introduction. We simply introduce species dynamics and artificial neural networks. In chapter 2, using the structure special function method, we have proven the existence and uniqueness of the solution to the stochastic cooperative model and estimate the upper rate of the solution .In chapter 3,we have proven the stability of the equilibrium point by stochastic Lyapunov function. In chapter 4, based on Lyapunov-Krasovskii functional theory and the linear matrix inequality (LMI) approach , we find a sufficient criteria of global exponential stability for static neural network models with time-varying delays and Markovian jumping parameters. In chapter 5, a sufficient condition is given to guarantee the global asymptotic robust stability for stochastic static neural network models with time-varying delays by using eigenvalue approach and Lyapunov-Krasovskii functional theory.