Dynamic Analysis of Stochastic Recurrent Neural Networks

Abstract

This paper addresses the issue of pth moment exponential stability of stochastic recurrent neural networks (SRNN) with time-varying interconnections and delays. With the help of the Dini derivative of the expectation of V (t, X(t)) "along" the solution X(t) of the model and the technique of Halanay-type inequality, some novel sufficient conditions on pth moment exponential stability of the trivial solution has been established. Conclusions of the development as presented in this paper have gone beyond some published results and are helpful to design stability of networks when stochastic noise is taken into consideration. An example is also given to illustrate the effectiveness of our results.

New p-th Moment Exponential Stability Criteria for FCNNs with Time-Varying Delays and Stochastic Effects

“…Lemma 2.5. [26] If there exists a constant 0 < u < 1 such that 0 < H 2 < uH 1 . Assume Z(t) is nonnegative continuous function on [t 0 − τ, t 0 ] and satisfies the following inequality…”

Stability of Coupled Systems of Stochastic Cohen-Grossberg Neural Networks with Time Delays, Impulses and Markovian Switching

“…There are many results on stability of stochastic neural networks with different model characteristics. The literature on this topic is extensive and here we give only few references: [11][12][13][14][15] cover the analysis of mean-square, pth moment and almost sure exponential stability of stochastic neural network models with and without impulsive effects. The results presented in [16][17][18][19] are examples of stability analysis of models with time delays, and the models considered in [20][21][22] also include Markovian switching.…”

pth moment exponential stability of stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays

“…Thus, the time-varying delays and continuous distributed delays are more appropriate to fuzzy cellular networks [18,19,31,44,48]. To the best of our knowledge, there are very few papers that deal with the stability of stochastic fuzzy Cohen-Grossberg neural networks with discrete and distributed delays [9,13,17,29,30,39,49].…”