Dynamical Behavior of a System of Second-Order Nonlinear Difference Equations

Abstract

This paper is concerned with local stability, oscillatory character of positive solutions to the system of the two nonlinear difference equationsxn+1=A+xn-1p/ynpandyn+1=A+yn-1p/xnp,n=0,1,…, whereA∈(0,∞),p∈[1,∞),xi∈(0,∞), andyi∈(0,∞),i=-1,0.

Dynamics of a System of Higher Order Difference Equations with Quadratic Terms

“…In [14], Bao investigated the local stability, oscillation of positive solutions to the system of difference equations…”

Qualitative study of a third order rational system of difference equations

“…Recently, the analysis of equilibrium solutions of various systems of nonlinear difference equations has been one of the main topics in the theory of dynamical systems (see [2,4,7,8,9,10,11,13,14,17,18,23,24,26,27] and the references cited therein). Difference equations and systems of difference equations play an important role in the analysis of mathematical models of many areas such as ecology, population dynamics, statistical problems, number theory, geometry, genetics in biology, economics, psychology, sociology, physics, engineering, economics (see [1,3,5,12,15,16,21,22]).…”

“…where the parameters A, B, b and the initial conditions x −2 , x −1 , x 0 are arbitrary non-negative real numbers. Motivated by the aforementioned study, our goal in this paper is to investigate the equilibrium points, the local asymptotic stability of these points, the global behavior of positive solutions, the existence of unbounded solutions and the existence of the prime two-periodic solutions of the following system (2) u n+1 = αu 2 n−1…”

“…, by the change of variables u n = β 1 γ 1 x n and v n = β γ y n with r = αβ 1 βγ 1 and s = α 1 β β 1 γ . We shall study the behavior of the solutions of the system (3) rather than system (2). Note that if (4) r = s and x −i = y −i for i = 0, 1, 2, in system (3), then the system (3) reduces into Eq.…”

Dynamical behavior of a system of three-dimensional nonlinear difference equations

“…In [2], Bao investigated the local stability, oscillation, and boundedness character of positive solutions of the system of difference equations…”