Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects. (10th February 2015)

• Record Type: Journal Article
• Authors: Liu, Haidong; Meng, Fanwei
• Other Names: He Xue Z. Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2015(2015)
• Publication Date: 2015-02-10
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2015/138984
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : We investigate the existence of periodic solutions for a predator-prey system with Holling function response and mutual interference. Our model is more general than others since it has both Holling type IV function and impulsive effects. With some new analytical tricks and the continuation theorem in coincidence degree theory proposed by Gaines and Mawhin, we obtain a set of sufficient conditions on the existence of positive periodic solutions for such a system. In addition, in the remark, we point out some minor errors which appeared in the proof of theorems in some published papers with relevant predator-prey models. An example is given to illustrate our results.