Periodic solutions for a delayed predator–prey system with stage‐structured predator on time scales

Periodic solutions for a delayed predator–prey system with stage‐structured predator on time scales

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Article ID: iaor20115649
Volume: 61
Issue: 11
Start Page Number: 3298
End Page Number: 3311
Publication Date: Jun 2011
Journal: Computers and Mathematics with Applications
Authors:
Keywords: predator-prey model
Abstract:

In this paper, a modified delayed predator–prey system with stage structure for predator is proposed and studied, which generalizes and incorporates as special cases some known models. With the help of continuation theorem based on the Gaines and Mawhin coincidence degree theory, we investigate the existence of periodic solutions for the proposed delayed predator–prey system with stage‐structured predator and two kinds of functional responses (called Holling III functional response and Beddington–DeAngelis functional response) on time scales. In particular, when the time scale is chosen as the set of the real numbers or the integers, the existence of the periodic solutions of the corresponding continuous‐time and discrete‐time models follows.

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