Permanence and almost periodic solutions for a single-species system with impulsive effects on time scales

Abstract

In this paper, we first propose a single-species system with impulsive effects on time scales and by establishing some new comparison theorems of impulsive dynamic equations on time scales, we obtain sufficient conditions to guarantee the permanence of the system. Then we prove a Massera type theorem for impulsive dynamic equations on time scales and based on this theorem, we establish a criterion for the existence and uniformly asymptotic stability of a unique positive almost periodic solution of the system. Finally, we give an example to show the feasibility of our main results. Our example also shows that the continuous time system and its corresponding discrete time system have the same dynamics. Our results of this paper are completely new.

Permanence and Almost Periodic Solutions for N‐Species Nonautonomous Lotka‐Volterra Competitive Systems with Delays and Impulsive Perturbations on Time Scales

“…In [23,24], the authors considered the existence and stability of periodic solutions for Lotka-Volterra systems. In [25], the authors investigated the permanence and almost periodic solutions for a singlespecies system with impulsive effects on time scales.…”

Dynamics of an almost periodic facultative mutualism model with time delays

“…Hence, if we consider the effects of the environmental factors, almost periodicity is sometimes more realistic and more general than periodicity. Recently, there are many scholars concerning the almost periodic oscillations of the ecosystems, see [4,9,10,14,15,20,27,29,30,31,32,33] and the references cited therein. Example 1.1.…”