IJPAM: Volume 61, No. 1 (2010)

EXISTENCE AND EXPONENTIAL STABILITY OF PERIODIC
SOLUTIONS OF IMPULSIVE HIGH-ORDER HOPFIELD
NEURAL NETWORK BOTH WITH DISCRETE AND
DISTRIBUTED DELAYS 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 and constructing some suitable Lyapunov functions, the periodicity and the exponential stability are investigated for a class of delayed high-order Hopfield neural networks with impulse on time scales, which are new and complement of previously known results. Finally, an example is given to show the effectiveness of the proposed method and results.

Received: May 3, 2010

AMS Subject Classification: 26A33

Key Words and Phrases: impulse, time scales, discrete delays, distributed delays, periodic solution, high-order Hopfield neural networks, Lyapunov function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 61
Issue: 1