Dynamics of a rational system of difference equations in the plane

TL;DR

This paper analyzes the behavior of a rational system of difference equations in two variables, examining how parameter variations influence stability, boundedness, periodicity, and asymptotic properties of solutions.

Contribution

It provides a comprehensive analysis of a specific rational difference system, detailing how parameters affect its global and local dynamics, including stability and periodic solutions.

Findings

Conditions for boundedness of solutions

Existence of periodic solutions under certain parameters

Stability criteria for equilibria

Abstract

We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of the system. In particular, we discuss the boundedness and the asymptotic behavior of the solutions, the existence of periodic solutions and the stability of equilibria.