IJPAM: Volume 62, No. 3 (2010)

GLOBAL EXPONENTIAL STABILITY AND EXISTENCE OF
PERIODIC SOLUTION AND ANTI-PERIODIC SOLUTION FOR
DELAYED COHEN-GROSSBERG BAM NEURAL NETWORKS
WITH IMPULSE ON TIME SCALES

Lili Zhao$^1$, Ping Liu$^2$
$^{1,2}$Department of Mathematics
Yunnan University
Kunming, Yunnan, 650091, P.R. CHINA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.Recently, many authors have studied the existence and global exponential stability of periodic solution and anti-periodic solution of many kinds of neural networks on time scales, by using the continuation theorem of coincidence degree theory, $M-$matrix theory and constructing some suitable Lyapunov functions. But, in this work, we only use the continuation theorem of coincidence degree theory, $M-$matrix theory to study the existence and exponential stability of periodic solution and anti-periodic solutions of a class of higher-order Cohen-Grossberg type neural networks with distributed delays and impulse on time scales. The activation functions $f_j,\,g_i$, are not assumed to be bounded in this work. Finally, an example is given to illustrate the effectiveness of our main results.

Received: June 21, 2010

AMS Subject Classification: 26A33

Key Words and Phrases: Cohen-Grossberg BAM neural networks, exponential stability, periodic solution, anti-periodic solutions, impulse, time scales

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 62
Issue: 3