Research On Global Stability And Finite Time Synchronization Of Stochastic Neural Networks

As a tool of artificial intelligence,stochastic neural networks introduce random change to neural networks and are widely used in various fields,such as optimization problems,risk control,oncology and bioinformatics.In this paper,based on Lyapunov stability theory,stochastic analysis theory and linear matrix inequalities(LMIs)technique,we study the porder exponential convergence,global asymptotic stability and finite-time synchronization of the stochastic neural networks.The main contents include:1.By using the theory of functional analysis and wick integral inequality analysis technique,we investigate p-order exponential convergence of stochastic neural networks.In hilbert space,the existence and uniqueness of the mild solution of system are proved.At the same time,based on the inequality analysis technique of the wick integral and famous inequality,we established the conditions for the p-order exponential convergence of the mild solution.Finally,according to the mathematical model of neural network,we established sufficient conditions for p-order exponential convergence for stochastic evolution differential equations driven by fractional brownian motion.2.Using Lyapunov functional theory and stochastic analysis theory,the problems of global stochastic asymptotic stability and p-order exponential stability of stochastic neural networks are explored.By designing appropriate Lyapunov functionals,we established sufficient conditions for the global stochastic asymptotical stability and p-order exponential stability of stochastic neural networks driven by fractional brownian motion.3.Under the extended filippov differential inclusion framework,the problem of finite time synchronization of a discontinuous stochastic neural network with semi-markov jump is explored.Applying non-smooth analysis theory with a generalized lyapunov-krasovskii functional with multiple integral terms and wirtinger-based multiple integral inequality analysis technique,together with properties of semi-markovian process,the finite-time synchronization conditions are addressed based on linear matrix inequalities(LMIs).