Stability Analysis Of Two Classes Of Stochastic Neural Networks With Multi-proportional Delays

Many results of neural networks only depend on time,without considering am-biguity and space.However,in real neural networks,the diffusion effect cannot be avoided when electrons move in asymmetric electromagnetic fields,so the state vari-ables change with time and space,and are not accurate.In this paper,we are interested in exponential stability for stochastic neural net-works with mixed delays.By constructing suitable Lyapunov-Krasovskii functionals and applying stochastic analysis theory.Ito's formula and Dynkin's formula,a mod-el of fuzzy stochastic neural networks with multi-proportional delays and distributed delays are established,in which multi-proportional delays are a kind of time-varying delays without boundaries,we derive novel sufficient conditions for mean-square ex-ponential input-to-state stability system.Then based on a new Lyapunov-Krasovskii function,Poincare inequality and stochastic analysis theory,we invesitigate the ex-ponential stability for stochastic reaction-diffusion BAM neural networks with with time-varying delays,multi-proportional delays and distributed delays,and a new suf-ficient condition to guarantee the stability of stochastic exponential is obtained.The results show that mixed delays and reaction diffusion do contribute to the exponential stability of the system under consideration,which is easy to verify,and less conservative than previous published literature on the exponential input-to-state stability of stochastic neural networks.Some examples are provided to illustrate the effectiveness of the theoretical results.