Delay Dependent Dynamics Analysis Of Two Types Of Hybrid Stochastic Delay Systems

As a kind of complex network with special structure,coupled systems are widely used in many fields.Stability and synchronization are two important dynamic properties of coupled systems,which have been thoroughly studied.It is noticed that systems in nature are inevitably disturbed by noise,which is necessary to consider stochastic factors when modelling systems.In addition,the external environment is variable,resulting in the fact that structure and parameters of many systems in the real world may be abrupt.Markov switching and regime switching diffusions have attracted the attention of scholars because of their ability to simulate the abrupt situation of the system.In addition,time delay is inevitable,and its existence will affect the stability and synchronization of the stochastic coupled system,so considering time delay is more in line with the requirements.However,most of the current studies on the dynamics of hybrid stochastic delay systems are not dependent on the information of time delay.In fact,the stability and synchronization criteria that rely on time delay can consider the information of time delay and thus have less conservatism.In this paper,considering stochastic disturbance,Markov switching,regime switching diffusions and time delay,and using Lyapunov function method,graph theory and some stochastic analysis techniques,the delay dependent dynamics properties of two kinds of hybrid stochastic delay systems are studied.Markov switching can well describe the abrupt changes in the structure and parameters of the system,therefore,in chapter 2,we study the delay dependent synchronization of stochastic delay systems with Markov switching on multi-weights network.By using the Lyapunov function method,a global Lyapunov functional is first constructed.Combining graph theory and inequality techniques,a series of sufficient criteria to ensure the synchronization of the system are given.In the theoretical application part,the delay dependent mean square asymptotical synchronization of stochastic delay coupled oscillators with Markov switching is studied,and a numerical example is given to illustrate the applicability of the theoretical results.Different from Markov switching,regime switching diffusions are diffusion jumping process with state dependent switching,which can better simulate the system of environment suffering emergency situation.Thus,in chapter 3,we analyze the delay dependent stability of stochastic delay systems with regime switching diffusions.Similarly,a global Lyapunov function is first constructed.By combining graph theory and some stochastic analysis techniques,several stability criteria dependent on time delay are obtained.Compared with the delay independent stability criterion,the obtained delay dependent stability criteria can make full use of the time delay information,so it is less conservative.Finally,the theoretical results are applied to stochastic delay coupled oscillators with regime switching diffusions.At the same time,a numerical example is given to illustrate the efficiency of the theoretical results.