Dynamical Analysis For Delayed Neural Networks

The delayed neural networks possessing rich dynamical behaviors are an important part of the delayed dynamic systems. Due to the important applications in optimization, signal processing, image processing, pattern recognition, associative memories and so on, the dynamical issues of delayed neural networks have attracted worldwide attention in recent years. In this thesis, by employing fixed point theorem, inequality technique, theory of stability, bifurcation theorem and theory of bifurcation control, the author investigates further the dynamical behaviors of delayed neural networks, which are described by the functional differential equations. The organization of this paper is as follows:In the first Chapter of this dissertation, the current status about stability of delayed dynamical systems, bifurcation, bifurcation control and delayed neural networks are summarized. Furthermore, the author introduces the main contents and originalities of this paper.The second Chapter introduces the basic concepts of dynamical systems including stability, bifurcation and control. The primary methods of stability, bifurcation and control are summarized comprehensively.The third Chapter studies the dynamics of a class of Cohen-Grossberg neural networks with variable and distributed delays. Without assuming the boundedness and Lipschitz condition on the activation function, some sufficient conditions ensuring the boundedness of solutions, the existence, uniqueness and exponential stability of equilibrium point are obtained by employing fixed-point theorem and applying the inequality technique.The fourth Chapter analyzes the Hopf bifurcation of a class of Hopfield neural networks with three delays. Moreover, the author proposes a new hybrid control strategy, in which parameter perturbation and time-delayed state feedback are used to control the Hopf bifurcation of the model, and some new results are obtained by the control method.The fifth Chapter summarizes the research work of this dissertation. Furthermore, the future research direction is made.