Wirtinger-based multiple integral inequality approach to synchronization of stochastic neural networks

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• 作者：Yue Zhang ^{yuezhang78@sina.com" class="auth_mail" title="E-mail the corresponding author} ; Cheng-De Zheng ; ^{chd4211853@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Stochastic neural networks ; Synchronization ; Jensen integral inequality ; Reciprocally convex combination ; Wirtinger-based integral inequality
• 刊名：Optik - International Journal for Light and Electron Optics
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：127
• 期：24
• 页码：12023-12042
• 全文大小：1122 K

文摘

This paper investigates the synchronization problem for a class of chaotic neural networks with discrete and unbounded distributed time delays under stochastic perturbations. Firstly, based on the Wirtinger-based double integral inequality, two novel inequalities are proposed, which are multiple integral forms of the Wirtinger-based integral inequality. Next, by applying the Jensen-type integral inequality for stochastic case and combining the Jensen integral inequality with the reciprocally convex combination approach, a delay-dependent criterion is developed to achieve the synchronization for the stochastic chaotic neural networks in the sense of mean square. In the case of no stochastic perturbations, by applying the reciprocally convex combination approach for high order case and a free-matrix-based inequality, novel delay-dependent conditions are established to achieve the synchronization for the chaotic neural networks. All the results are based on dividing the bounding of activation function into two subintervals with equal length. Finally, two numerical examples are provided to demonstrate the effectiveness of the theoretical results.