IJPAM: Volume 62, No. 2 (2010)

GLOBALLY EXPONENTIAL STABILITY AND EXISTENCE
OF ANTIPERIODIC SOLUTION OF A CLASS OF
HIGHER-ORDER HOPFIELD NEURAL NETWORKS WITH
DISTRIBUTED DELAYS AND 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.On time scales, by using the continuation theorem of coincidence degree theory, $M-$matrix theory and constructing some suitable Lyapunov functions, some sufficient conditions are obtained for the existence and exponential stability of anti-periodic solutions of a class of higher-order Hopfield neural networks with distributed delays and impulse, which are new and complement of previously known results. Finally, an example is given to illustrate the effectiveness of our main results.

Received: May 20, 2010

AMS Subject Classification: 26A33

Key Words and Phrases: higher-order Hopfield neural networks, exponential stability, anti-periodic solutions, distributed delays, impulse, time scales

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 62
Issue: 2