Study On The Stability Of Two Class Of Stochastic Time-Delay Neural Network Models

Stochastic time-delay neural network models have been widely used in signal processing,pattern recognition,static image processing,associative memory and combinatorial optimization.In real systems,due to the random effect in neurons and the speed of switching system,we inevitably need to consider the delay recursion problem,which is also the main reason for the vibration and instability of neural network.Most scholars in the study of random recursive neural networks with delay,are demanding the conclusion formed,such as requiring neuron activation function is bounded,differentiable,and has the properties such as monotonicity,the strict requirements in practice,not only limits the range of application of stochastic delay neural network,and applied quite difficult.Therefore,in order to further broaden the application scope of stochastic time-delay neural networks,this paper starts with the research on existing constraints and selectively extends some of them.By using Lyapunov stability theory,stochastic analysis technique,Perron-Frobenius theorem,Razumikhin stability theorem and so on,we study the almost everywhere stability of Markov switched stochastic delay recursive neural network model and Cohen-Grossberg stochastic delay neural network model.For the almost everywhere stability problem of Markov switched stochastic delay recursive neural networks,the main difficulty is to find the condition that meets the stability of the equation,which needs to be based on certain assumptions,and this paper is to find more indirect assumptions to meet the stability condition.By using Lyapunov stability theory,It?formula and Perron-Frobenius theorem,we obtain sufficient conditions for the almost everywhere stability of markov switched recursive neural networks with stochastic delays.For the problem of almost everywhere stability of Cohen-Grossberg stochastic delay neural networks,this paper uses Razumikhin’s stability theorem,inequality techniques and other methods to obtain the conditions of almost everywhere stability of this kind of models without activating the differential,monotonicity and symmetry of the connection matrix.Finally,an example is analyzed and a reliable verification is given.Finally,Lyapunov function method and stochastic analysis technique are used to obtain the P moment exponential stability of markov switched stochastic time-delay recursive neural networks,and the results are verified by an example.