Investigation Of Some Issues Of Stochastic Cohen-Grossberg Neural Networks Models

In recent years, the dynamical issues of stochastic delayed neural networks haveattracted worldwide attention. Many interesting stability criteria for the equilibriumsolutions of stochastic delayed neural networks have been obtained. In this thesis,we investigate the pth moment exponential stability and the almost sure exponentialstability of the equilibrium solutions for stochastic Cohen-Grossberg neural networks(CGNN) with time-varying delays and unbounded distributed delays. The thesis con-sists of four chapters.As the introduction, in Chapter One, the background and development of thestudy of the stability for stochastic neural networks are presented. The motivationsand outline of this work are also given in this chapter.In Chapter Two, some fundamental knowledge, including the basic concepts ofstochastic di?erential equation, stochastic processes, Brown motions, Ito? integral andIto? formula, is brie?y introduced.In Chapter Three, the stability of the equilibrium solutions for stochastic CGNNwith time-varying delays are studied. With the help of the semimartingale conver-gence theorem, some su?cient criteria are established for the almost sure exponentialstability of the system. Using Ito? formula, the Dini-derivative and the technique ofsome inequalities, we obtain some su?cient criteria to check the pth moment exponen-tial stability for a general stochastic CGNN with time-varying delays, then, applyingBurkholder-Davids-Gundy inequality and Borel-Cantell's lemma, a family of su?cientconditions is given for checking the almost sure exponential stability of this model.Finally, in Chapter Four, the stability of the equilibrium solutions for stochasticCGNN with unbounded distributed delays are investigated. Without assuming thesmoothness, by constructing suitable Lyapunov function, employing the semimartin-gale convergence theorem and the technique of some inequalities, we obtain some suf-ficient criteria to check the almost exponential stability of the model. An example isalso given to illustrate the e?ectiveness of the obtained results.