Stability analysis of a discrete ecological model
Q. Din
E. M. Elsayed
Department of Mathematics, Faculty of Basic and Applied Sciences, University of PoonchRawalakot, Pakistan
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Computational Ecology and Software
ISSN 2220-721X
http://www.iaees.org/publications/journals/ces/online-version.asp
2014
4
2
89
103
International Academy of Ecology and Environmental Sciences
Hong Kong
14 January 2014
20 February 2014
1 June 2014
population models
difference equations
steady-states
boundedness
local and global character
In this paper, we study the qualitative behavior of following discrete-time population model: x(n+1)=a+bx(n)+rx(n-1)exp(-y(n)),y(n-1)=g+ey(n)+hy(n-1)exp(-x(n)), where parameters a, b, r, g, e, h and initial conditions x(0), x(-1), y(0), y(-1) are positive real numbers. More precisely, we investigate the existence and uniqueness of positive equilibrium point,boundedness character, persistence, local asymptotic stability, global behavior and rate of convergence of unique positive equilibrium point of this model. Some numerical examples are given to verify our theoretical results.
DOI 10.0000/issn-2220-721x-compuecol-2014-v4-0008
http://www.iaees.org/publications/journals/ces/articles/2014-4(2)/stability-analysis-of-a-discrete-ecological-model.pdf