With The Global Exponential Synchronization Of The Hybrid Coupler And Discrete Time-varying Delay Neural Network

Synchronization, as an important dynamical phenomenon, is receiving an increasing research attention due to its extensive application. In this thesis, we aim to deal with the global exponential synchronization problem for an array of discrete-time neural networks with mixed coupling and time-varying delays. The dynamics of system under consideration is governed by:Firstly, we define the distance between a point and the synchronization manifold. Furthermore, by resorting to properties of the matrix Kronecker product, and constructing novel Lyapunov-Krasoskii functional, we derive the sufficient conditions under which the considered coupled neural networks are globally exponentially synchronized. These conditions are checked by Matlab software. This thesis is organized as follows.In section 1, the background and significance of research on neural networks are expounded; and we conclude this section by introducing our major results in this thesis.In section 2, the related notation and system (3) to be considered are introduced.In section 3, some definitions and related lemmas are presented. And system (3) is rewritten in a compact form in order to facilitate our analysis. Furthermore, the activation functions are given subject to a weaker assumption, i.e., the so-called nonlinear sector condition. And it will lead to less conservative results.In section 4, we firstly prove an important lemma for the main theory. And the criteria for the global exponential synchronization is derived based on the matrix Kronecker product properties and Lyapunov theory.In section 5, numerical simulations are presented to demonstrate the effectiveness of the addressed approach.