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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 674027, 11 pages
http://dx.doi.org/10.1155/2015/674027
Research Article

A New Approach to Global Stability of Discrete Lotka-Volterra Predator-Prey Models

1Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
2Department of Mathematics, University of Ulsan, Ulsan 680-749, Republic of Korea

Received 24 March 2015; Accepted 20 May 2015

Academic Editor: Ryusuke Kon

Copyright © 2015 Young-Hee Kim and Sangmok Choo. 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

An Euler difference scheme for a three-dimensional predator-prey model is considered and we introduce a new approach to show the global stability of the scheme. For this purpose, we partition the three-dimensional space and calculate the sign of the rate change of population of species in each partitioned region. Our method is independent of dimension and then can be applicable to other dimensional discrete models. Numerical examples are presented to verify the results in this paper.