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Uniform persistence of asymptotically periodic multispecies competition predator-prey systems with Holling III type functional response. (English) Zbl 1084.92036

Introduction: Recently, the well-known predator-prey systems with Holling III type functional response have been studied by many authors, their works are concerned with two or three species models. However, in nature, multispecies systems are common and universal. Simultaneously, they are more complicated and realistic than the two or three species. A recent paper of C. Chen and F. Chen [J. Biomath. 19, 136–140 (2004)] is based on a multispecies competition predator-prey system. They have obtained a sufficient condition of uniform persistence in a non-autonomous periodic multispecies competition predator-prey system with Holling III type functional response. Conversely, the research work about asymptotically periodic multispecies competition predator-prey systems with Holling III type functional response is few at present.
The main purpose of this paper is to study the persistence of asymptotically periodic multispecies competition predator-prey systems with Holling III type functional response. In these systems, the competition among predator species and among prey species are simultaneously considered. In the view of reality, we improve the result of the paper of Chen and Chen. At the same time we obtain conditions for uniform strong persistence.

MSC:

92D40 Ecology
34D99 Stability theory for ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
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References:

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