Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays

Abstract

In this paper, the problem of stability analysis for a class of impulsive stochastic Cohen-Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M -matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic Cohen-Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.

Exponential synchronization of memristive Cohen–Grossberg neural networks with mixed delays

“…Some other models, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory neural networks, are special cases of the model (Kamel and Xia 2009;Mahdavi and Kurths 2013;Yang et al 2008Yang et al , 2011. Stability and synchronization of continuous Cohen-Grossberg neural networks with or without discrete and distributed delays were studied in the literature (Zhu and Cao 2010;He and Cao 2008;Song and Wang 2008). Recently, stability of Cohen-Grossberg neural networks with discontinuous activations were considered in Chen and Song (2010) and Lu and Chen (2008).…”

Diversities of periodic solutions for a class of ecological model

“…It has gained increasing interest in many applications to biological systems (see, e.g. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]). Motivated by aforementioned discussions, in this article, we propose the following more general nonautonomous models with nonmonotonic functional response g:…”

Exponential stability analysis for delayed stochastic Cohen-Grossberg neural network

“…Results in 5,6 suggested that the neural networks can be stabilized or destabilized by certain stochastic inputs, which implies that it is important to consider the noise effects in the stability analysis for the neural networks. Recently, the study of stochastic neural networks has drawn much attentions from researchers all over the world and some results can be found in 7,8,9,10,11,12,13,22 and the references cited therein 15,16,17,19,21 . But for the study of stochastic CGNN, up till now, there are only a few results 10,11,14,20 .…”