Advances in Difference Equations
Volume 2004 (2004), Issue 4, Pages 279-290
doi:10.1155/S1687183904308101

Stability for delayed generalized 2D discrete logistic systems

Chuan Jun Tian1 and Guanrong Chen2

1College of Information Engineering, Shenzhen University, Shenzhen 518060, China
2Department of Electronic Engineering, City University of Hong Kong, Hong Kong

Received 28 August 2003; Revised 19 February 2004

Copyright © 2004 Chuan Jun Tian and Guanrong Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with delayed generalized 2D discrete logistic systems of the form xm+1,n=f(m,n,xm,n,xm,n+1,xm−σ,n−τ) , where σ and τ are positive integers, f:ℕ02×ℝ3→ℝ is a real function, which contains the logistic map as a special case, and m and n are nonnegative integers, where ℕ0={0,1,…} and ℝ=(−∞,∞). Some sufficient conditions for this system to be stable and exponentially stable are derived.