With Simultaneous Analysis Of Mixed-delay Neural Network

In this thesis, the synchronization problems are discussed for two classes of coupled delayed neural networks. The first one is the system of neural networks with drive-response structure and control inputs; and the other one is the coupled system of an array of identical neural networks. These models involve both discrete and distributed time delays, and the stochastic disturbance is also considered in our investigation. The related activation functions are assumed to satisfy so called sector nonlinear condition, which is quite general and can reduces the conservativeness for the LMIs-based approach. This thesis consists of three chapters, and is organized as follows:The opening chapter gives an introduction to the related background and the latest progress in the synchronization and control problem for delayed neural networks. We conclude this chapter with the formulation of problems to be investigated.In Chapter 2, the synchronization problem of the drive-response system is discussed for delayed neural networks with mixed time-delays. The delayed neural networks , either with or without reaction-diffusion, are studied in turn. The system under consideration contains time-varying discrete time delay and bounded distributed time-delay, the activation functions are assumed to satisfy the sector nonlinear condition, and the external disturbance in response systems is considered as well. By constructing new Lyapunov-Krasovskii functionals, some sufficient criteria are derived to guarantee for the given coupled system to be globally asymptotically synchronized.In Chapter 3, the synchronization problem of an array of stochastic delayed neural networks is investigated. By exploiting Kronecker product and linear matrix inequality, some sufficient conditions, under which the array of stochastic delayed neural networks can achieve global synchronization in the mean square, are derived. Note that the LMIs can be easily and effectively solved by using the Matlab LMI toolbox. Here the considered neural networks are quite general, which contain parameter uncertainties, distributed time-delay, stochastic disturbance and nonlinear coupling. The assumption on activation functions is relaxed without assuming to be of Lipschitz type or Sigma type. The sufficient conditions are obtained for the array of stochastic delayed neural networks to be robustly globally asymptotically synchronized in the mean square. In the case of constant time-delay, the array the mean-square exponential synchronization problem of stochastic delayed neural networks is further dealt with. Our work is an extension to the related results in the existing literature.