IJPAM: Volume 20, No. 1 (2005)

GLOBAL STABILITY OF A CLASS OF DELAYED
NEURAL NETWORK MODELS UNDER
DYNAMICAL THRESHOLDS

Fei-Yu Zhang$^1$, Ren-Hu Wang$^2$, Xing-Xue Yan$^3$
$^1$Department of Mathematics
Hexi University Zhangye
Gansu, 734000, P.R. CHINA
$^1$e-mail: zhfy@hxu.edu.cn


Abstract.In this paper, we study dynamical behavior of a class of cellular neural networks system with distributed delays under dynamical thresholds. By using homeomorphism map, M-matrix and Lyapunov functions, some new criteria ensuring the existence, uniqueness, global asymptotic stability and global exponential stability of equilibrium point are derived. In the results, we do not require the activation function to be bounded, differentiable, and monotonic nondecreasing. Moreover, the symmetry of the connection matrix is not also necessary. Our criteria generalize and improve some known results in the literature.

Received: February 28, 2005

AMS Subject Classification: 34A40, 34K13, 34K14, 34K20, 92B20

Key Words and Phrases: equilibrium, Homeomorphism, M-matrix, Lyapunov function, Globally asymptotically stable, Globally exponentially stable

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 20
Issue: 1