Qualitative behavior of an anti-competitive system of third-order rational difference equations

In this paper, our aim is to study the equilibrium points, local asymptotic stability, global behavior of an equilibrium points and rate of convergence of an anti-competitive system of third-order rational difference equations of the form: x(n+1)=ay(n-2)/[b+rx(n)x(n-1)x(n-2)], y(n+1)=cx(n-2)/[d+hy(n...

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Bibliographic Details
Published in:Computational ecology and software 2014-06, Vol.4 (2), p.104-115
Main Authors: Din, Q, Qureshi, M.N, Khan, A.Q
Format: Article
Language:English
Subjects:
Asymptotic properties
Computer programs
Convergence
Convergence (Mathematics)
Difference equations
global character
Initial conditions
Mathematical models
Mathematical research
rate of convergence
rational difference equations
Software
Stability
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Summary:In this paper, our aim is to study the equilibrium points, local asymptotic stability, global behavior of an equilibrium points and rate of convergence of an anti-competitive system of third-order rational difference equations of the form: x(n+1)=ay(n-2)/[b+rx(n)x(n-1)x(n-2)], y(n+1)=cx(n-2)/[d+hy(n)y(n-1)y(n-2)], n=0,1,2,..., where the parameters a, b, c, d, r, h and initial conditions x(0), x(-1), x(-2), y(0), y(-1), y(-2) are positive real numbers. Some numerical examples are given to verify our theoretical results.
ISSN:2220-721X
2220-721X
DOI:10.0000/issn-2220-721x-compuecol-2014-v4-0009