Stability Analysis And Application Of Stochastic Neural Networks With Time Delays

Artificial neural network,as one of the research hotspots in the field of artificial intelligence,is widely used in phase structure,pattern recognition,associative memory,wireless communication and other fields.Stochastic neural networks refer to the addition of stochastic perturbation on the basis of neural networks,which may make the original system from stable to unstable,or from unstable to stable.Therefore,it is necessary to analyze and explain the stability of stochastic neural networks from the perspective of mathematics.Based on the research of stability at home and abroad,this paper studies the dynamic properties of markovian jumping uncertain stochastic Cohen-Grossberg neural networks with multi-proportional delays.Firstly,after giving seven necessary assumptions,the mean square polynomial stability of markovian jumping uncertain stochastic Cohen-Grossberg neural networks with multi-proportional delays is studied in two steps.The first step is to extend the existing results of mean square polynomial stability analysis of stochastic pantograph differential equations to stochastic differential equations with multiple proportional delays by using the generalized Ito formula,the local Lipschitz condition and stopping time argument;In the second step,the sufficient condition for the mean square polynomial stability of the system is given by using matrix inequalities and the research result of stochastic differential equations with multiple proportional delays.In addition,in order to further improve the theoretical research,the numerical examples are given for the main criteria,and the numerical simulation is carried out by using R software through Euler Maruyama method and discrete probability distributions sampling.The simulation results of the examples verify the feasibility of the given conditions again.Secondly,an external input is introduced to the markovian jumping uncertain stochastic Cohen-Grossberg neural networks with multi-proportional delays,and an exponential decay constraint is added to the activation function.Under the local Lipschitz condition,the criterion of mean square exponential input-to-state stability for stochastic differential equations with multiple proportional delays is given firstly,and then the sufficient condition of mean square exponential input-to-state stability is given by using this criterion and matrix inequality technique.In order to make the theoretical research more complete,a numerical example is also given here,and the rationality of the given criterion is illustrated by the simulation results of the example.Finally,starting from the application of neural networks with multi-proportional delays,the potential application scenarios of markovian jumping uncertain stochastic Cohen-Grossberg neural networks with multi-proportional delays are discussed.