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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 375890, 11 pages
http://dx.doi.org/10.1155/2014/375890
Research Article

Stability Analysis of a System of Exponential Difference Equations

1Department of Mathematics, University of Poonch Rawalakot, Rawalakot 12350, Pakistan
2Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan

Received 14 May 2014; Accepted 14 July 2014; Published 24 July 2014

Academic Editor: Garyfalos Papashinopoulos

Copyright © 2014 Q. Din et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the boundedness character and persistence, existence and uniqueness of positive equilibrium, local and global behavior, and rate of convergence of positive solutions of the following system of exponential difference equations: , , where the parameters , and for and initial conditions , and are positive real numbers. Furthermore, by constructing a discrete Lyapunov function, we obtain the global asymptotic stability of the positive equilibrium. Some numerical examples are given to verify our theoretical results.