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.
Highlights
IntroductionMany authors [1,2,3,4,5,6,7] have extensively considered different types of predator-prey system
In recent years, many authors [1,2,3,4,5,6,7] have extensively considered different types of predator-prey system
We investigate the existence of periodic solutions for a predator-prey system with Holling function response and mutual interference
Summary
Many authors [1,2,3,4,5,6,7] have extensively considered different types of predator-prey system. When Hassell studied the capturing behavior between the hosts (some bees) and parasite (a kind of butterfly), he noted that the hosts had the tendency to leave each other when they met, which interfered the hosts capturing effects He found that the mutual interference would be stronger while the populations of the parasite became larger and he introduced the concept of mutual interference constant m. Many authors began to study some kinds of predator-prey systems with mutual interference; see [9,10,11,12] for more details. Wang and Zhu [13] investigated a Volterra model with mutual interference and a Holling II type functional response ẋ. We consider the following predator-prey system of Holling type IV function response with mutual interference and impulsive effects:.
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