周期多比例时滞细胞神经网络全局渐近稳定性的平均准则  

An Average Criterion for Global Asymptotic Stability of Periodic Multi-Proportional Delayed Cellular Neural Networks

作　　者：王小伟[1] 胡霁芳 肖玉柱[1] 宋学力[1] 

机构地区：[1]长安大学理学院,陕西西安

出　　处：《应用数学进展》2016年第4期705-715,共11页Advances in Applied Mathematics

基　　金：国家自然科学基金(11201038);陕西省青年科技新星项目(2014KJXX-55);长安大学中央高校基本科研业务费专项资金(310812163504,310812151004)的资助。

摘　　要：本文致力于研究带有周期系数和多比例时滞细胞神经网络的全局渐近稳定性。首先,通过研究微分不等式的渐近稳定性,我们给出一类周期泛函微分方程的渐近稳定性准则;其次,利用获得的稳定性结果和非线性测度方法,我们给出该类神经网络的全局渐近稳定性准则,我们的研究结果是现有相关结果的部分推广;最后,一个例子被提供以说明我们结果的正确性。This paper is devoted to studying global asymptotic stability of cellular neural networks with periodic coefficients and multi-proportional delays. Firstly, through studying the asymptotic stability of the differential inequality, we give the asymptotic stability criterion of a class of periodic functional differential equations. Secondly, we obtain an integral average criterion for global asymptotic stability of the cellular neural networks by means of the result we obtain and the nonlinear measure method, and our study result is partial generalization of some existing results. Finally, we use an example to illustrate the correctness of our result.

关 键 词：全局渐近稳定性 细胞神经网络 周期系数 多比例时滞 积分平均准则 

分 类 号：O1[理学—数学]