Dynamical behavior of Pielou's difference system with exponential term

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.