Exponential Stability Analysis Of Stochastic Fuzzy Cellular Neural Networks With Delays

Since cellar neural networks(CNNs) was introduced in 1980s by Chua and Yang, this model has received increasing interest due to its promising potential applications in many fields such as pattern recognition, signal processing, parallel computing and combinatorial optimization. However, there have shortcomings in itself. Some researchers introduced fuzzy logical theory into cellar neural networks to form fuzzy cellar neural networks(FCNNs), which as results, maximizes the advantages of cellar neural networks and fuzzy set theory. FCNNs have potential application in many fields such as machine intelligence, control, decision analysis and so on. These applications heavily depend on the dynamical behaviors, especially the stability of neural networks.In practical application, some factors that have great influence on the stability of FCNNs such as delay and impulsion. At present, some results about the stabil-ity of FCNNs with delays and impulsion are obtained. In fact, the transmission of neurons cell in the brains is noisy process. So, we should consider the stability of FCNNs in the noise environments. In recent years, there are few about stochastic effect on the stability of FCNNs. Furthermore, several type of stochastic FCNNs haven't been discussed by now. The paper mainly consider the stability of FCNNs with stochastic perturbation, which including time—varying delays, distributed de-lays and impulsion. By using stochastic processes and analysis, some criteria to judge the the stability of FCNNs affected by stochastic perturbation are obtained, which make up and enrich the result in this areas and has some theoretical and practical value. The paper is organized as follows:In chapter 1, we mainly focus on the background of CNNS and FCNNs, and research status of their stability.In chapter 2, a class of stochastic fuzzy cellular neural networks with time—varying delays is considered. Sufficient conditions for the mean square exponential stability are obtained by using Lyapunov functional and stochastic analysis, which is easy to satisfy. An example is provided to demonstrate the usefulness of the proposed criteria.In chapter 3, the exponential stability of a class of stochastic fuzzy cellular neural networks with distributed delays is investigated in this paper. By using an-alytic methods such as Lyapunov functional, Ito's formula, inequality techniques and nonegative semimartingale convergence theorem, the sufficient conditions guar-anteeing the almost sure and mean square exponential stability of its equilibrium solution are respectively obtained. For illustration, an example is given to show the feasibility of results.In chapter 4, by using analytic methods such as Lyapunov functional, Ito's formula, inequality techniques. The mean square exponential stability of a class of impulsive stochastic fuzzy cellular neural networks with distributed delays is inves-tigated, the sufficient conditions guaranteeing the mean square exponential stability of its equilibrium solution are obtained, which make up for gaps in stability of such stochastic models, At the same time, some inferences and remarks were prospered which greatly extend the previous results. At last the conclusion is illuminated through an example.