On some stability problems of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays

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• 作者：Biljana Tojtovska^a ; ¹ ; ^{biljana.tojtovska@finki.ukim.mk" class="auth_mail} ; Svetlana Jankovi膰^b ; ² ; ^{svjank@pmf.ni.ac.rs" class="auth_mail}
• 关键词：Lyapunov function ; Impulsive stochastic neural networks ; Moment stability ; Almost sure stability ; General decay function
• 刊名：Applied Mathematics and Computation
• 出版年：15 July 2014
• 年：2014
• 卷：239
• 期：Complete
• 页码：211-226
• 全文大小：1129 K

文摘

This paper covers the topic of both the p  th moment (p猢?$p猢?/mo><mn>2</mn>$) and almost sure stability of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays. We partially use a known result on exponential stability of impulsive stochastic functional differential systems, based on the Razumikhin type technique, and extend it to the case of stochastic neural networks using the Lyapunov function method and a Gronwall type inequality. Additionally, we consider the stability with respect to a general decay function which includes exponential, but also more general lower rate decay functions as the polynomial and the logarithmic ones. This fact gives us the opportunity to study general decay almost sure stability, even when the exponential one cannot be discussed. Suitable examples which support the theory are also presented.