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Global dynamics of a competitive system of rational difference equations
Author(s) -
Khan A. Q.,
Qureshi M. N.
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3392
Subject(s) - mathematics , uniqueness , equilibrium point , stability (learning theory) , convergence (economics) , order (exchange) , character (mathematics) , exponential stability , dynamics (music) , rate of convergence , point (geometry) , mathematical economics , mathematical analysis , nonlinear system , differential equation , geometry , economics , channel (broadcasting) , physics , engineering , finance , quantum mechanics , machine learning , economic growth , computer science , acoustics , electrical engineering
In this paper, we study the qualitative behavior of a competitive system of second‐order rational difference equations. More precisely, we investigate the boundedness character, existence and uniqueness of positive equilibrium point, local asymptotic stability and global stability of the unique positive equilibrium point and rate of convergence of positive solutions of the system. Some numerical examples are given to verify our theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.