| At present,the existing results on coupled neural networks focus on the nonlinear dynamics of nodes.The effects of the complexity of network structure are seldom considered.However,the coupling structure of a network plays an important role in the dynamic characteristics of the network.In applications,a network or system is often affected by some abrupt factors,such as stochastic disturbances in the environment,changes in the connection among subsystems,and so on.Thus,the coupling structure of the network and the coupling strength between nodes change randomly.The jump of this large-scale network can be classified into the research category of stochastic switched neural networks.The research on this kind of system has important theoretical value and practical significance.This thesis addresses finite-time and fixed-time synchronization of a general class of coupled switched neural networks(SNNs)with time delays subject to stochastic disturbances.Considering two types of switching rules in this class of coupled SNNs:(1)intraSNN state-dependent switching and(2)inter-SNN Markovian switching.This class of coupled SNNs with time delays subject to stochastic disturbances is a special stochastic system,which has two dynamic forms: mode and state.The mode of the system is described by a continuous-time and discrete-state Markov chain.The state of the system is described by a state equation in each mode.The state equation is represented by a stochastic differential equation.The switching among different modes is subject to the Markov chain.This thesis uses a leaderless synchronization control scheme and transforms the synchronization problem for the system into the stability problem for the error system.Therefore,it is necessary to analyze the stability of stochastic differential equations with Markovian switching.Firstly,according to the existing It(?)-Doeblin formula of the process with rapid switching and the definition of the Markov chain,the It(?)-Doeblin formula for Markov process is derived.By using Lyapunov stability theory and stochastic analysis,sufficient conditions for asymptotic stability in probability of stochastic differential equations with time delays and Markovian switching are obtained.Furthermore,the sufficient conditions for finitetime stability of stochastic differential equations with time delays and Markov switching are analyzed.Secondly,the control-law is designed to stabilize the state-dependent SNN.By introducing parameter uncertainty and stochastic disturbance into the state-dependent SNN,the robust stability of the controlled state-dependent SNN is obtained.Finally,according to the leaderless synchronization scheme,a contro-law is designed to achieve finite-time synchronization of coupled SNNs with stochastic disturbances and time delays.An improved control-law is designed for fixed-time synchronization.The sufficient conditions for fixed-time synchronization of coupled SNNs with stochastic disturbance and time delays are obtained.Several upper bounds of synchronization settling time are derived and their pros and cons are evaluated.Furthermore,two numerical examples are given to illustrate the viability of the theoretical results. |
