ASYMPTOTIC BEHAVIOR OF A SYSTEM OF NONLINEAR DIFFERENCE EQUATIONS
Asymptotic behavior of a system of nonlinear difference equations is the shape of its solution around the equilibrium point. In this paper, we investigate the asymptotic behavior of the equilibrium point of a system of nonlinear difference equations
where A ∈ (0,∞) and x-1, x0, y-1, y0 are positive numbers. By the linearization method and the comparative method, we have studied the stability of the equilibrium point under certain parametric conditions. Some numerical examples are given to illustrate the results we obtained.
G. Papaschinopoulos, C.J. Schinas, “On a system of two difference equations”. J. Math. Anal. Appl., 219(2), 1998, pp. 415–426.
G. Papaschinopoulos, C.J. Schinas, “On the system of two nonlinear difference equations x(n+1)=A+x(n-1)/y(n), y(n+1)=A+y(n-1)/x(n)”. Int. J. Math. Math. Sci., 23(12), 2000, pp. 839–848.
M. Gümüṣ, “The global asymptotic stability of a system of difference equations”. J. Difference Equ. Appl., 24(6), 2018, pp. 976-991.
H. Bao, “Dynamical behavior of a system of second-order nonlinear difference equations”. Int. J. Differ. Equ., 2015, Article ID 679017, 7 pages.
E. Camuozis, G. Papaschinopoulos, “Global asymptotic behavior of positive solutions on the system of rational difference equations x(n+1)=1+x(n)/y(n-m), y(n+1)=1+y(n)/x(n-m)”. Appl. Math. Lett., 17(6), 2004, pp. 733-737.
T.H. Thai, V.V. Khuong, “Stability analysis of a system of second-order difference equations”. Math. Methods Appl. Sci., 39, 2016, pp. 3691–3700.
I. Okumus, Y. Soykan, “Dynamical behavior of a system of three-dimensional nonlinear difference equations”. Advances in Difference Equations, 223, 2018, 15 pages.
V.L. Kocic, G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications. 1993, Chapman & Hall, London.
E. Camouzis, G. Ladas, Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjecture. 2008, Chapman & Hall, London.