含脉冲的随机延迟细胞神经网络的均方指数稳定性与周期解(英)

doi:10.3969/j.issn.1005-3085.2016.01.009

工程数学学报 ›› 2016, Vol. 33 ›› Issue (1): 91-105.doi: 10.3969/j.issn.1005-3085.2016.01.009

含脉冲的随机延迟细胞神经网络的均方指数稳定性与周期解(英)

李浩¹, 李毓²

1- 广西师范大学数学与统计学院，桂林 541004
2- 信阳师范学院经济学院，信阳 464000

收稿日期:2014-03-25 接受日期:2015-03-09 出版日期:2016-02-15 发布日期:2016-04-15
基金资助:
河南省教委重大基金项目 (14B910001)；河南省哲学社会科学规划项目 (2014BJJ069).

Mean Square Exponential Stability and Periodic Solutions of Stochastic Delay Cellular Neural Networks with Impulses

LI Hao¹, LI Yu²

1- School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004
2- School of Economics, Xinyang Normal University, Xinyang 464000

Received:2014-03-25 Accepted:2015-03-09 Online:2016-02-15 Published:2016-04-15
Supported by:
The Major Project of Foundation of Educational Committee of Henan Province (14B910001); the Planning Project of Philosophy and Social Science of Henan Province (2014BJJ069).

摘要/Abstract

摘要： 本文主要研究一类带离散延迟和脉冲的随机细胞神经网络(SDCNNswI)的均方指数稳定性和周期解的存在性．首先，用庞加莱收缩理论分析了SDCNNswI的周期解存在条件；其次，用李雅谱诺夫函数、随机分析理论和Young不等式推出了几个定理，给出了保证SDCNNswl的周期解具有均方指数稳定性的几个充分条件，其中只包含SDCNNswI的几个控制参数，通过简单的代数方法即可验证．最后，通过两个例子说明了所提出准则的有效性．

关键词: 布朗运动, Young不等式, It\^{o}公式, 李雅谱诺夫函数, 指数稳定性, 细胞神经网络

Abstract:

For a class of stochastic cellular neural networks with discrete delays and impu-lses (SDCNNswI), this paper discusses their exponential stability and the existence of periodic solutions. Firstly, Poincare contraction theory is utilized to derive the conditions to guarantee the existence of periodic solutions of SDCNNswI. Next, Lyapunov function, stochastic analysis theory and Young inequality are develo-ped to derive some theorems. These theorems provide several sufficient conditions to guarantee that the periodic solutions of SDCNNswI are mean square exponentially stable. These sufficient conditions only include the governing parameters of SDCNNswI and can be easily checked by simple algebraic methods. Finally, two examples are given to demonstrate the usefulness of the obtained results.

Key words: Brownian motion, Young inequality, It$\hat{\rm o}$ formula, Lyapunov function, exponential stability, cellular neural networks

中图分类号:

O193

李浩, 李毓. 含脉冲的随机延迟细胞神经网络的均方指数稳定性与周期解(英)[J]. 工程数学学报, 2016, 33(1): 91-105.

LI Hao, LI Yu. Mean Square Exponential Stability and Periodic Solutions of Stochastic Delay Cellular Neural Networks with Impulses[J]. Chinese Journal of Engineering Mathematics, 2016, 33(1): 91-105.

[1]	张冬洁, 张卫国, 雍燕, 李想. 河床流体模型方程扭状孤波解的渐近稳定性[J]. 工程数学学报, 2019, 36(2): 165-178.
[2]	苏丽娟, 周立群. 一类具比例时滞细胞神经网络反周期解的指数稳定性[J]. 工程数学学报, 2017, 34(2): 143-154.
[3]	赵宁, 周立群. 一类具多比例时滞递归神经网络的全局指数稳定性[J]. 工程数学学报, 2016, 33(5): 450-462.
[4]	宋学力, 赵盼, 王小伟. 具时滞和脉冲影响的同类商品价格波动模型的全局指数稳定性(英)[J]. 工程数学学报, 2015, 32(2): 307-316.

含脉冲的随机延迟细胞神经网络的均方指数稳定性与周期解(英)

Mean Square Exponential Stability and Periodic Solutions of Stochastic Delay Cellular Neural Networks with Impulses

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 4

编辑推荐

Metrics

本文评价