Existence and Stability Property of Almost Periodic Solutions in Discrete Almost Periodic Systems

On the Stability in Almost Periodic Discrete Systems

In this paper, the discrete system which is described by difference equations xn+1 = fn(xn), fn(0) = 0, n = 0, 1, 2, . . . . is considered. This system has the trivial (zero) solution xn = 0. Sufficient conditions of its asymptotic stability are obtained in the cases when functions fn(x) are almost periodic in n. Copyright c ©2005 IFAC

Existence of Periodic and Almost Periodic Solutions of Abstract Retarded Functional Difference Equations in Phase Spaces

Almost Periodic Solutions of Prey-Predator Discrete Models with Delay

The purpose of this article is to investigate the existence of almost periodic solutions of a system of almost periodic Lotka-Volterra difference equations which are a prey-predator system x1 n 1 x1 n exp{b1 n −a1 n x1 n −c2 n ∑n s −∞ K2 n−s x2 s }, x2 n 1 x2 n exp{−b2 n − a2 n x2 n c1 n ∑n s −∞ K1 n − s x1 s } and a competitive system xi n 1 xi n exp{bi n − aiixi n − ∑l j 1,j / i ∑n s −∞ Kij n...

Almost Periodic and Periodic Solutions of Difference Equations

I t is easy to see that for every point (y, N) in WXI there is a solution (n) of (1) that satisfies <1>(N) =y. This solution is defined and unique on some set N^nKN*» where N<» is maximal. (That is, either iV» = °o or ^ i V ^ — l) (£W.) The solution may or may not be continuable for nƒ> rc)> 0^w<iV o o(^ , / ) , be the soluti...

Existence and Exponential Stability of Positive Almost Periodic Solutions for a Model of Hematopoiesis

By employing the contraction mapping principle and applying Gronwall-Bellman's inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solution for nonlinear impulsive delay model of hematopoiesis.