IJPAM: Volume 39, No. 1 (2007)

EXPONENTIAL PERIODICITY OF THE DISCRETE-TIME
RECURRENT NEURAL NETWORKS WITH VARIABLE
DELAYS AND IMPULSES

Zhenjiang Zhao$^1$, Qiankun Song$^2$
$^1$Department of Mathematics
Huzhou Teachers College
Zhejiang, 313000, P.R. CHINA
e-mail: zhaozjcn@163.com
$^2$Department of Mathematics
Chongqing Jiaotong University
Chongqing, 400074, P.R. CHINA
e-mail: qiankunsong@163.com


Abstract.In this paper, the problems on the existence and global exponential stability of periodic solution are investigated for the impulsive discrete-time recurrent neural network with periodic coefficients and time-varying delays. By using analytical methods, inequality technique and $M$-matrix theory, several sufficient conditions are obtained to ensure the existence, uniqueness and global exponential stability of periodic solution for the addressed neural network. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper improve and extend some previously related results. An example with simulation is given to show the effectiveness of the obtained results.

Received: March 28, 2007

AMS Subject Classification: 39A11, 92B20

Key Words and Phrases: discrete-time recurrent neural network, variable delay, impulse, global exponential stability, periodic solution

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 39
Issue: 1