Electron. J. Diff. Eqns., Vol. 2004(2004), No. 29, pp. 1-16.

Periodic solution and global exponential stability for shunting inhibitory delayed cellular neural networks

Anping Chen, Jinde Cao, & Lihong Huang

For a class of neural system with time-varying perturbations in the time-delayed state, this article studies the periodic solution and global robust exponential stability. New criteria concerning the existence of the periodic solution and global robust exponential stability are obtained by employing Young's inequality, Lyapunov functional, and some analysis techniques. At the same time, the global exponential stability of the equilibrium point of the system is obtained. Previous results are improved and generalized. Our results are shown to be more effective than the existing results. In addition, these results can be used for designing globally stable and periodic oscillatory neural networks. Our results are easy to be checked and applied in practice.

Submitted December 24, 2003. Published February 26, 2004.
Math Subject Classifications: 34K13, 34K20, 92B20.
Key Words: Periodic solutions, global exponential stability, Poincare mapping, shunting inhibitory delay cellular neural networks, Lyapunov functionals.

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Anping Chen
Department of Mathematics
Xiangnan University
Chenzhou, Hunan 423000, China
email: chenap@263.net
Jinde Cao
Department of Mathematics
Southeast University
Nanjing 210096, China
email: jdcao@seu.edu.cn   jdcao@cityu.edu.hk
  Lihong Huang
College of Mathematics and Econometrics
Hunan University, Hunan 410082, China
email: lhhuang@hnu.edu.cn

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