Mean square exponential stability of stochastic delay cellular neural networks
Mean square exponential stability of stochastic delay cellular neural networks
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DOI：
10.14232/ejqtde.2013.1.34
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发表时间：
2013
影响因子：
1.1
通讯作者：
Yingxin Guo
中科院分区：
文献类型：
--
作者：
Yingxin Guo
随机神经网络的动力学行为已经成为一个新的研究和应用课题，如优化，控制和图像处理（见[1-12]）。显然，寻找这类神经网络的稳定性判据成为一个有吸引力的重要研究问题。在文献[1-5]中，对随机时滞Hopfield神经网络和随机Cohen-Grossberg神经网络，利用线性矩阵不等式方法建立了神经网络全局稳定的充分条件。特别地，文[2]利用变分参数方法和随机分析方法，给出了保证平衡解指数稳定的充分条件。然而，目前文献中关于随机效应对时滞细胞神经网络稳定性影响的研究还很少。研究了时滞随机细胞神经网络（SDCNNs）平衡点的指数稳定性。在文献[13]中，利用广义李雅普诺夫函数、随机分析、Young不等式方法和Poincare压缩理论，得到了SDCNN周期解存在和稳定的条件.与线性矩阵不等式（LMI）方法[13]，[15]和变参数方法不同，Young不等式方法首次被发展来研究SDCNN的稳定性。这些充分条件改进和推广了文献[1]中的早期工作。[18，19]，并且它们包含SDCNN的控制参数，因此与[13-17]的结果相比，可以通过简单的代数方法轻松检查它们。最后，通过一个例子说明了本文结果的有效性.
The dynamical behaviors of stochastic neural networks have appeared as a novel subject of research and applications, such as optimization, control, and image processing(see [1-12]). Obviously, finding stability criteria for these neural networks becomes an attractive research problem of importance. Some well results have just appeared, for example, in [1-5], for stochastic delayed Hopfield neural networks and stochastic Cohen-Grossberg neural networks, the linear matrix inequality approach is utilized to establish the sufficient conditions on global stability for the neural networks. In particular, in [2], by using the method of variation parameter and stochastic analysis, the sufficient conditions are given to guarantee the exponential stability of an equilibrium solution. However, there are few results about stochastic effects to the stability property of cellular neural networks with delays in the literature today. In this paper, exponential stability of equilibrium point of stochastic cellular neural networks with delays(SDCNNs) is investigated. Following [13], that activation functions require Lipschitz conditions and boundedness, by utilizing general Lyapunov function, stochastic analysis, Young inequality method and Poincare contraction theory are utilized to derive the conditions guaranteeing the existence of periodic solutions of SDCNNs and the stability of periodic solutions. Different from the LMI (linear matrix inequality) approach [13], [15] and variation parameter method, the Young inequality method is firstly developed to investigate the stability of SDCNN. These sufficient conditions improve and extend the early works in Refs. [18,19], and they include those governing parameters of SDCNNs, so they can be easily checked by simple algebraic methods, comparing with the results of [13-17]. Furthermore, one example is given to demonstrate the usefulness of the results in this paper.