数学物理学报 ›› 2013, Vol. 33 ›› Issue (4): 777-786.

• 论文 • 上一篇    下一篇

具反应扩散项和Neumann边界条件的脉冲变时滞细胞神经网络的全局指数稳定性

张雨田|罗琦   

  1. 南京信息工程大学 数学与统计学院 南京 210044;南京信息工程大学 信息与控制学院 南京 210044
  • 收稿日期:2012-04-12 修回日期:2013-02-20 出版日期:2013-08-25 发布日期:2013-08-25
  • 基金资助:

    国家自然科学基金(60904028, 61174077)资助

Global Exponential Stability of Impulsive Reaction-Diffusion Cellular Neural Networks with Time-Varying Delays and Neumann Boundary Condition

 ZHANG Yu-Tian, LUO Qi   

  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044; School of Information and Control, Nanjing University of Information Science and Technology, Nanjing 210044
  • Received:2012-04-12 Revised:2013-02-20 Online:2013-08-25 Published:2013-08-25
  • Supported by:

    国家自然科学基金(60904028, 61174077)资助

摘要:

讨论了一类具变时滞、反应扩散项和Neumann边界条件的脉冲细胞神经网络的稳定性. 利用Gronwall-Bellman-type脉冲积分不等式和Poincar'e不等式, 获得了一些新的与时滞和扩散因素有关的全局指数稳定性判据, 并给出了指数收敛速度估计. 最后两个例子证明了结论的有效性.

关键词: 全局指数稳定性, 反应扩散, 脉冲, 时滞, 积分不等式

Abstract:

This work addresses the stability of a class of impulsive cellular neural networks with time-varying delays, reaction-diffusion terms and Neumann boundary condition. By using Gronwall-Bellman-type impulsive integral inequality and
Poincar´e inequality as well as the properties of diffusion operator, we develop some new sufficient conditions ensuring the global exponential stability of equilibrium point. Moreover, the estimate of exponential convergence rate is derived and shown to be associated with diffusion and time delays. Finally, two examples are illustrated to demonstrate the effectiveness of our obtained results.

Key words: Global exponential stability, Reaction diffusion,  Impulsive, Delay, Integral inequality

中图分类号: 

  • 45M10