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VOL. 53 | 2009 Global behavior of a two-dimensional monotone difference system
Momoe Inoue, Hideaki Matsunaga

Editor(s) Saber Elaydi, Kazuo Nishimura, Mitsuhiro Shishikura, Nobuyuki Tose

Abstract

We investigate global behavior of solutions of a nonlinear difference system $$ x_{n+1} = px_n (1 + y_n),\quad y_{n+1} = qy_n (1 + x_n),\quad n = 0, 1, 2, \dots, $$ where parameters $p$, $q$ and initial values $x_0$, $y_0$ are positive. We give sufficient conditions for every solution of the system to be unbounded and sufficient conditions for the global stable manifold of the positive equilibrium to exist, which is a unbounded separatrix for the system. Some related conjectures are also given.

Information

Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1179.39020
MathSciNet: MR2582412

Digital Object Identifier: 10.2969/aspm/05310129

Rights: Copyright © 2009 Mathematical Society of Japan

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