Global Behavior of a System of Second-Order Rational Difference Equations

Year 2021, Volume: 4 Issue: 3, 150 - 162, 30.09.2021

Phong MAİ NAM

https://doi.org/10.33434/cams.938775

Abstract

In this paper, we consider the following system of rational difference equations

$$x_{n+1}=\frac{a+x_n}{b+c{y}_n+d{x}_{n-1}}$$

, yn+1=α+ynβ+γxn+ηyn−1

, n=0,1,2,...xn+1=a+xnb+cyn+dxn−1, yn+1=α+ynβ+γxn+ηyn−1, n=0,1,2,...

where $a,b,c,d,\alpha ,\beta ,\gamma ,\eta \in (0,\infty )$ and the initial values $x_{-1},x_0,y_{-1},y_0\in (0,\infty )$. Our main aim is to investigate the local asymptotic stability and global stability of equilibrium points, and the rate of convergence of positive solutions of the system.

Keywords

Equilibrium points, local stability, global behavior, rate of convergence, positive solutions

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