Dynamical behavior of Pielou's difference system with exponential term

TL;DR

This paper analyzes a Pielou's difference system with exponential terms, establishing conditions for boundedness, persistence, and global stability of solutions, supported by numerical examples.

Contribution

It introduces new sufficient conditions for stability and boundedness of a Pielou's difference system with exponential terms, using Lyapunov functionals.

Findings

Solutions are bounded and persistent under certain conditions.

Global asymptotic stability of equilibria is established.

Numerical examples confirm theoretical results.

Abstract

In this paper, we investigate a type of Pielou's difference system with exponential term $$ y_{n+1}=\frac{az_n}{p+z_{n}}e^{-y_n},\; \;\;\;\;\; z_{n+1}=\frac{by_n}{q+y_{n}}e^{-z_n}. $$ where the parameters $a,b,p,q, $ are positive real numbers and the initial values $y_0,z_0$ are arbitrary nonnegative real numbers. Using the mean value theorem and Lyapunov functional skills, we obtained some sufficient conditions which guarantee the boundedness and persistence of the solution, and global asymptotic stability of the equilibriums. Moreover, two numerical examples are given to elaborate on the results.