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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 138984, 12 pages
Research Article

Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects

School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Received 19 August 2014; Revised 17 January 2015; Accepted 18 January 2015

Academic Editor: Xue Z. He

Copyright © 2015 Haidong Liu and Fanwei Meng. 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.


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.