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Journal of Applied Mathematics
Volume 2005, Issue 2, Pages 153-169
http://dx.doi.org/10.1155/JAM.2005.153

Periodicity in a ratio-dependent predator-prey system with stage structure for predator

College of Mathematics and Computer Science, Fuzhou University, Fujian, Fuzhou 350002, China

Received 27 August 2003; Revised 11 September 2004

Copyright © 2005 Hindawi Publishing Corporation. 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

With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the global existence of positive periodic solutions of a delayed ratio-dependent predator-prey system with stage structure for predator. The approach involves some new technique of priori estimate. For the system without delay, by constructing a suitable Lyapunov function, some sufficient conditions which guarantee the existence of a unique global attractive positive periodic solution are obtained. Those results have further applications in population dynamics.