Studies On Stability And Almost Periodicity Of Several Classes Of Recurrent Neural Networks With Delays

Recurrent neural networks with delays, which have been successfully applied in pattern recognition, signal processing, associative memory, optimization problem and so on, are important dynamical systems with delays. The main reason lies principally in that recurrent neural networks with delays have complicated dynamic behavior, including stability, periodicity, chaos and so on. This paper mainly studies the stability and almost periodicity of recurrent neural networks with delays.This paper has five parts.Chapter 1 summarizes the development of neural networks, the current status and meaning of dynamics of recurrent neural networks with delays, while introducing the main contents and originalities of this paper.In Chapter 2, based on Homeomorphism theory, Lyapunov stability theory, combining with the techniques of Ho lderinequality and linear matrix inequality, the essay explores a class of the more general cellular neural networks model with constant delays, and establishes the new sufficient criteria ensuring the existence,uniqueness and global exponential stability of equilibrium point. The criteria established here are all given in terms of linear matrix inequality, which are helpful to be directly verified by linear matrix inequality toolbox. Furthermore, the outcomes of the chapter remove the restriction on the boundedness of the activation function, include or improve part of the conclusions drawn from the existing literatures.Chapter 3 analyzes the existence,uniqueness and global exponential stability of almost periodic solution of two-order Cohen-Grossberg neural networks with constant delays. By employing Schauder fixed-point theory,exponential dichotomy theory and the technique of differential inequality, the novel sufficient criteria are established. The outcomes of the chapter improve part of the conclusions drawn from the existing literatures. Furthermore, this method can be also applied to the two-order Cohen- Grossberg neural networks model with variable delays.Chapter 4 consists of the discussions of the stability for stochastic fuzzy cellular neural networks with delays. By constructing the different Lyopunov functionals, using non-negative semi-martingale convergence theory and Ito? formula, and combining with the technique of inequality, the novel sufficient criteria are established for ensuring the almost sure exponential stability of equilibrium point, which provide the theoretical supports for the designing and application of the networks.In the last chapter, the essay concludes the research work of this paper, and looks forward to the future research directions.