Wirtinger-based multiple integral inequality approach to synchronization of stochastic neural networks
Wirtinger-based multiple integral inequality approach to synchronization of stochastic neural networks
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DOI：
10.1016/j.ijleo.2016.09.094
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发表时间：
2016-12
期刊：
影响因子：
3.1
通讯作者：
Yue Zhang;Chengde Zheng
中科院分区：
文献类型：
--
作者：
Yue Zhang;Chengde Zheng
本文研究了一类具有离散和无界分布式时滞的混沌神经网络在随机扰动下的同步问题。首先，在基于Wirtinger的二重积分不等式的基础上，提出了两个新的不等式，它们是基于Wirtinger的积分不等式的多重积分形式。接下来，通过将Jensen型积分不等式应用于随机情况，并将Jensen积分不等式与互凸组合方法相结合，提出了一种延迟相关准则，以实现随机混沌神经网络在均方意义上的同步。在没有随机扰动的情况下，通过应用高阶情况的互凸组合方法和基于自由矩阵的不等式，建立了新颖的延迟相关条件来实现混沌神经网络的同步。所有结果都是基于将激活函数的边界划分为两个长度相等的子区间。最后，提供两个数值例子来证明理论结果的有效性。
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.