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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 368176, 8 pages
http://dx.doi.org/10.1155/2013/368176
Research Article

Periodic Solutions for Gause-Type Ratio-Dependent Predator-Prey Systems with Delays on Time Scales

School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, Henan 471023, China

Received 28 February 2013; Accepted 27 May 2013

Academic Editor: Qiru Wang

Copyright © 2013 Xiaoquan Ding 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 is devoted to periodic Gause-type ratio-dependent predator-prey systems with monotonic or nonmonotonic numerical responses on time scales. By using a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of periodic solutions. In particular, our results improve and generalize some known ones.