Research On Dynamics Of Delayed Neural Networks

Delayed neural networks are extensively applied in those fields such as signal processing, moving image processing, artificial intelligence, global optimizing, and etc. While the dynamical characteristics of delayed neural networks include stable, unstable, oscillatory and chaotic behaviors, the dynamical issues of delayed neural networks have attracted worldwide attentions in recent years. Recently, many interesting results on global stability (including absolute stability, asymptotic stability, robust stability, and exponential stability, etc.) criteria for the equilibriums or periodic solutions, Hopf bifurcation and chaos of delayed neural networks have been obtained.This dissertation mainly focuses on the global stability, Hopf bifurcation, chaos control and synchronization of delayed neural networks. Specifically, the main contents are as follows:1. Global robust stability analysis of delayed cellular neural networksBy constructing a novel Lyapunov-Krasovskii functional, and by applying the linear matrix inequality technique and S-procedure, a less conservative global robust stability criterion for cellular neural networks with constant delay is derived. In addition, global robust stability criterion for cellular neural networks with time-varying delay is also achieved.2. Global exponential stability analysis of delayed Cohen-Grossberg neural networksBy constructing appropriate Lyapunov-Krasovskii functional for Cohen-Grossberg neural networks with const delay and time-varying delay respectively, based on the linear matrix inequality technique, some easily verified sufficient conditions for global exponential stability are established. In addition, the exponential convergence degrees of the models are discussed in detail.3. Hopf bifurcation analysis of Hopfield neural networks with mixed delaysThe Hopfield neural networks with discrete delay is generalized to a model with both discrete and distributed delays. It is found that this system undergoes a sequence of Hopf bifurcations by analyzing its associated transcendental characteristic equation. By applying the center manifold theorem and the normal form theory, formulae for determining the direction of Hopf bifurcation and the stability and period of bifurcating periodic solutions are derived.4. Chaos control of delayed Hopfield neural networksAn appropriate full delayed feedback controller is proposed to stabilize the chaotic trajectory of delayed Hopfield neural network to its unstable equilibrium, the feedback gain matrix and an upper bound of the controller time delay are determined simultaneously. For the delayed Hopfield neural networks with uncertain parameters, an adaptive control model is proposed and asymptotic stability condition in analytic form of such model is presented, the chaotic trajectory can be brought to the trajectory of a desired system.5. Chaos synchronization of delayed Hopfield neural networksBased on the Lyapunov stability theory and the linear matrix inequality technique, a sufficient condition for chaos complete synchronization of bi-directional coupled delayed Hopfield neural networks is obtained and a control strategy is proposed. By applying the adaptive technique and system identification technique to chaos lag synchronization issue of delayed Hopfield neural networks with uncertain parameters, a sufficient condition for chaos lag synchronization is derived, and the parameter estimation law is obtained.