Dynamics Behaviors Research For A Class Of Stochastic Competitive Neural Networks With S-type Distributed Delays

The dynamics behaviors for a class of stochastic competitive neural networks with S-typedistributed delays are discussed in this paper, including global asymptotic stability, mean squareexponential robust stability and exponential synchronization. Firstly, a brief overview of artificialneural network, especially the background and progress of competitive neural network areintroduced. Secondly, global asymptotic stability for a class of competitive neural networks withS-type distributed delays is studied, which are described by functional differential equation groups.Homotopy invariance, topological degree theory and homeomorphism mapping are used to gainthe existence and uniqueness of equilibrium solutions to network. Then asymptotic stability ofnetworks is proved and the criterion for asymptotic stability is given. Thirdly, stochastic factorsare considered in competitive neural networks with S-type distributed delays and a class ofstochastic competitive neural networks with S-type distributed delays is obtained, described bystochastic functional differential equation groups. Global mean square exponential robust stabilityis researched by Lyapunov functional methods and stochastic analysis technique. Sufficientcondition for global exponential robust stability is given and then MATLAB simulation exampleshows the validity of the conclusions. Fourthly, exponential synchronization of a class ofstochastic competitive neural networks with S-type distributed delays is discussed in the paper.Mean square exponential synchronization behavior between driving system and driven system isresearched by Lyapunov-Krasovskii functional and stochastic analysis skills. An algebraic criteriaof exponential synchronization has been given and some results have been improved. At last, theprospect for research will be given.