Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1

Global dynamics of a system of nonlinear difference equations was investigated, which had five kinds of equilibria including isolated points and a continuum of nonhyperbolic equilibria along the coordinate axes. The local stability of these equilibria was analyzed which led to nine regions in the pa...

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Main Authors: Keying Liu, Peng Li, Weizhou Zhong
Format: Article
Language:English
Published: Wiley 2017-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2017/1295089
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author Keying Liu
Peng Li
Weizhou Zhong
author_facet Keying Liu
Peng Li
Weizhou Zhong
author_sort Keying Liu
collection DOAJ
description Global dynamics of a system of nonlinear difference equations was investigated, which had five kinds of equilibria including isolated points and a continuum of nonhyperbolic equilibria along the coordinate axes. The local stability of these equilibria was analyzed which led to nine regions in the parameters space. The solution of the system converged to the equilibria or the boundary point (+∞,0) or (0,+∞) in each region depending on nonnegative initial conditions. These results completely described the behavior of the system.
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institution Kabale University
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publishDate 2017-01-01
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series Discrete Dynamics in Nature and Society
spelling doaj-art-8e64642e40914c038628a5c64cadf77e2025-02-03T05:54:12ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/12950891295089Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1Keying Liu0Peng Li1Weizhou Zhong2School of Economics and Finance, Xi’an Jiaotong University, Xi’an 710061, ChinaSchool of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450045, ChinaSchool of Economics and Finance, Xi’an Jiaotong University, Xi’an 710061, ChinaGlobal dynamics of a system of nonlinear difference equations was investigated, which had five kinds of equilibria including isolated points and a continuum of nonhyperbolic equilibria along the coordinate axes. The local stability of these equilibria was analyzed which led to nine regions in the parameters space. The solution of the system converged to the equilibria or the boundary point (+∞,0) or (0,+∞) in each region depending on nonnegative initial conditions. These results completely described the behavior of the system.http://dx.doi.org/10.1155/2017/1295089
spellingShingle Keying Liu
Peng Li
Weizhou Zhong
Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1
Discrete Dynamics in Nature and Society
title Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1
title_full Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1
title_fullStr Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1
title_full_unstemmed Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1
title_short Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1
title_sort global dynamics of rational difference equations xn 1 xn xn 1 q ynyn 1 and yn 1 yn yn 1 p xnxn 1
url http://dx.doi.org/10.1155/2017/1295089
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