Stability Analysis Of Stochastic Fuzzy Cellular Neural Networks

Artificial neural networks(usually known as neural networks) are nonlinearself-adaptive information processing systems built up by numerous processingunits and are designed for dealing with data by simulating the thinking patternsof human beings. Traditional certain neural networks have been perfectlydeveloped for imitating abstract thinking patterns. However, in the area ofuncertain intelligence, this work is still at the stage of exploration. Since thetwo most fundamental kinds of uncertainty are randomness and fuzziness, threeclasses of stochastic fuzzy neural networks are studied in this thesis.In Chapter1, we briefly introduce the history and current situation of theresearch in stochastic fuzzy neural networks. We also explaine several neuralnetworks which are common in practice, and conclude the main contributionsand innovations of this thesis.Chapter2is the preparation part. Both the theory of stochastic differentialequations and the theory of fuzzy logic are introduced in this chapter.In Chapter3, we aim at analyzing a class of stochastic fuzzy cellular neuralnetworks(SFCNNs) with time-varying delays. This class of SFCNNs is widelyused in areas such as signal processing, pattern recognition, associativememory and image processing. By constructing suitable Lyapunov functionaland originally applying linear matrix inequalities(LMI), we are able to give thefinal results for the globally asymptotic stability presented in the form of LMI.In Chapter4, we focuse on a class of SFCNNs with Markovian jumping andmixed time delays(including time-varying delays and distributed delays). Basedon traditional SFCNNs, this model also takes delays of different forms and thepossibility of the network switching between various modes into consideration.By constructing suitable Lyapunov functional and applying stochasticinequalities, we derive two kinds of stabilities: the almost surely exponentialstability and the exponential stability in the mean square.In Chapter5, we study a class of time-varying delayed stochastic fuzzyneural networks with neutral type. This kind of networks is also an innovationof this thesis---fuzzy logic is introduced into traditional neutral stochasticfuzzy neural networks and uncertainty is described by the “if---then” rules. Byusing Ito formula, stochastic analysis and inequality techniques, we obtain the sufficient conditions of its almost surely exponential stability.In the last section of each chapter, a numerical example is given to assurethe effectiveness of the results.At last, a conclusion is made to explain the main contributions and thefuture work that can be done for each model.