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

TL;DR

This paper studies a single-species model with impulsive effects on time scales, establishing conditions for permanence and the existence of stable almost periodic solutions, unifying continuous and discrete dynamics.

Contribution

It introduces new comparison theorems and a Massera type theorem for impulsive dynamic equations on time scales, providing novel criteria for permanence and stability.

Findings

Established sufficient conditions for system permanence.

Proved existence and stability of positive almost periodic solutions.

Demonstrated the equivalence of continuous and discrete time dynamics.

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 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.