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Stability analysis of a system of second‐order difference equations
Author(s) -
Thai Tran Hong,
Khuong Vu Van
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.3816
Subject(s) - mathematics , uniqueness , character (mathematics) , order (exchange) , stability (learning theory) , convergence (economics) , persistence (discontinuity) , rate of convergence , mathematical analysis , pure mathematics , geometry , channel (broadcasting) , geotechnical engineering , electrical engineering , finance , machine learning , computer science , engineering , economics , economic growth
In this paper, we study the boundedness character and persistence, existence and uniqueness of the positive equilibrium, local and global behavior, and the rate of convergence of positive solutions of the following system of rational difference equationsx n + 1 =α 1 + β 1y na 1 + b 1y n − 1,y n + 1 =α 2 + β 2x na 2 + b 2x n − 1,where the parameters α i , β i , a i , b i for i ∈{1,2} and the initial conditions x −1 , x 0 , y −1 , y 0 are positive real numbers. Some numerical example are given to verify our theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.