Abstract and Applied Analysis
Volume 2012 (2012), Article ID 940287, 19 pages
http://dx.doi.org/10.1155/2012/940287
Research Article

Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed System

Yong-Hui Xia,1,2 Xiang Gu,1 Patricia J. Y. Wong,3 and Syed Abbas4

1Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
2Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, 2000 Maribor, Slovenia
3School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798
4School of Basic Sciences, Indian Institute of Technology Mandi, Mandi 175001, India

Received 11 August 2012; Accepted 27 August 2012

Academic Editor: Jifeng Chu

Copyright © 2012 Yong-Hui Xia 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

This paper gives an application of Mawhin’s coincidence degree and matrix spectral theory to a predator-prey model with M-predators and N-preys. The method is different from that used in the previous work. Some new sufficient conditions are obtained for the existence and global asymptotic stability of the periodic solution. The existence and stability conditions are given in terms of spectral radius of explicit matrices which are much different from the conditions given by the algebraic inequalities. Finally, an example is given to show the feasibility of our results.