Dynamics Analysis Of Several Classes Of Neural Network Models

In this thesis, we deal with some important properties of the dynamic behaviors ofseveral classes of neural networks. A set of stability, bifurcation and periodic oscillationresults for several general neural network models is derived by employing Brouwer's fixedpoint theorem, matrix theory, inequality analysis and a continuation theorem of the coinci-dence degree.As the introduction, in Chapter One, the background and history of neural networksare brie?y addressed. The motivations and outline of this work are also given in thischapter.In Chapter Two, some notations, definitions and lemmas are listed.In Chapter Three, we establish some sufficient conditions for the global exponentialstability of a unique equilibrium for a general Cohen-Grossberg neural network with time-varying delays. Brouwer's fixed point theorem, matrix theory and inequality analysis areemployed. Our results are all independent of the delays and maybe more convenient todesign a circuit network.In Chapter Four, without assuming the smoothness, monotonicity and boundedness ofthe activation functions, some sufficient conditions are derived for checking the periodicoscillation and global exponential stability of two classes of neural network models. Ourmethods are based on the continuation theorem of the coincidence degree, a priori estimate,and some differential inequalities.Then, in Chapter Five, under the help of matrix theory, a continuation theorem ofthe coincidence degree and inequality analysis, we make a further investigation of twoclass of neural networks: cellular neural network(CNN) and Cohen-Grossberg neural net-work(CGNN). A family of sufficient conditions is given for checking global exponentialstability and the existence of periodic solutions. These results may have important leadingsignificance in the design and applications of globally stable CNN and periodic oscillatoryCGNN. Our results extend and improve some earlier publications.Finally, in Chapter Six, two classes of planar systems with three and four delays arestudied. At appropriate parameter values, linear stability and Hopf bifurcation includingits direction and stability are established in this chapter. The main tools to obtain ourresults are the normal form method and the center manifold theory introduced by Hassard.Simulations show that the theoretically predicted values are in excellent agreement with...