pth Moment Exponential Stability of Stochastic Cohen-Grossberg Neural Networks With Time-varying Delays

Abstract

The pth moment exponential stability of stochastic Cohen-Grossberg with time-varying delays is investigated in this paper. A set of novel sufficient conditions on pth moment exponential stability are given for the considered system by using the wellknown Razumikhin-type theorem. Finally, two examples with their numerical simulations are provided to show the correctness of our analysis.

Stability analysis of non-autonomous stochastic Cohen–Grossberg neural networks

“…Let p = 2, then the Corollary 3.4 is the main result (Theorem 1) in [24]. In [28], the authors studied pth moment exponential stability for system (26) also by using the Razumikhintype theorem. Unfortunately, the proof of the main result (Theorem 1) in [28] may not be correct for condition (H 2 ) and the Lyapunov function applied in [28] is incorrect.…”

“…On the other hand, during hardware implementation, time delays are often the source of oscillation and instability in neural networks. Although various issues of stability of delayed neural networks have been extensively investigated by many authors in the past two decades, the issue of stochastic effects on the stability has been not studied until recent years (see [21][22][23][24][25][26][27][28][29][30][31][32]). In [21], Liao and Mao studied mean square exponential stability and instability of cellular neural networks (CNNs).…”

“…In [22], almost sure exponential stability for a class of stochastic CNNs with discrete delays was investigated. In [24,28], exponential stability of stochastic CGNNs with time-varying delays via Razumikhin-type were investigated. In [23], Wan and Sun investigated mean square exponential stability of stochastic delayed Hopfield neural networks (HNNs).…”

pth Moment stability of stochastic neural networks with Markov volatilities

“…Recently, some related results have been proposed in [9,11,18]. It is worth noting that the Markovian switching was not taken into account in many literature [9,11,[18][19][20]. However, as we know now, the hybrid systems with Markov chains have been used to model many practical systems, in which the abrupt changes in their structure may be occurred.…”

New Results on Robust Exponential Stability of Uncertain Stochastic Neural Networks with Mixed Time-Varying Delays

“…Therefore, the robust stability analysis for uncertain stochastic neural networks with delays has been extensively studied, see [15][16][17][18][19][20][21][22] for examples. As discussed in [23][24][25], distributed delays should be incorporated into the model due to the fact that there may exist a distribution of propagation delays over a period of time in some cases.…”