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

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.