Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 423193, 12 pages
Research Article

Existence of Positive Periodic Solutions for a Nonautonomous Generalized Predator-Prey System with Time Delay in Two-Patch Environment

1Department of Mathematics and Physics, Nanhua University, Hengyang 421001, China
2Department of Applied Mathematics, Hunan University, Changsha 410082, China

Received 25 November 2011; Accepted 26 January 2012

Academic Editor: Vimal Singh

Copyright © 2012 Huilan Wang 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.


By using continuation theorem of coincidence degree theory, sufficient conditions of the existence of positive periodic solutions are obtained for a generalized predator-prey system with diffusion and delays. In this paper, we construct a V-function to make the prior estimation for periodic solutions, which makes the discussion more concise. Moreover, to compute the mapping's topological degree, a polynomial function matrix is constructed straightforwardly as a homotopic mapping for the generalized one, which improves the methods of computation on topological degree for a generalized mapping.