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

Authors : Phong MAİ NAM

Pages : 150-162

Doi:10.33434/cams.938775

View : 13 | Download : 4

Publication Date : 2021-09-30

Article Type : Research Paper

Abstract :In this paper, we consider the following system of rational difference equations x n + 1 = a + x n b + c y n + d x n − 1 ,   y n + 1 = α + y n β + γ x n + η y n − 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 , α , β , γ , η ∈ insert ignore into journalissuearticles values( 0 , ∞ ); a,b,c,d,α,β,γ,η∈insert ignore into journalissuearticles values(0,∞); and the initial values x − 1 , x 0 , y − 1 , y 0 ∈ insert ignore into journalissuearticles values( 0 , ∞ ); x−1,x0,y−1,y0∈insert ignore into journalissuearticles values(0,∞); . 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