# American Institute of Mathematical Sciences

October  2016, 21(8): 2867-2881. doi: 10.3934/dcdsb.2016077

## Global dynamics of three species omnivory models with Lotka-Volterra interaction

 1 Department of Mathematics, Tamkang University, Tamsui, Taipei County 25137 2 Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China 3 Department of Mathematics, Tamkang University, Tamsui, New Taipei City 25137, Taiwan

Received  June 2016 Revised  July 2016 Published  September 2016

In this work, we consider the community of three species food web model with Lotka-Volterra type predator-prey interaction. In the absence of other species, each species follows the traditional logistical growth model and the top predator is an omnivore which is defined as feeding on the other two species. It can be seen as a model with one basal resource and two generalist predators, and pairwise interactions of all species are predator-prey type. It is well known that the omnivory module blends the attributes of several well-studied community modules, such as food chains (food chain models), exploitative competition (two predators-one prey models), and apparent competition (one predator-two preys models). With a mild biological restriction, we completely classify all parameters. All local dynamics and most parts of global dynamics are established corresponding to the classification. Moreover, the whole system is uniformly persistent when the unique coexistence appears. Finally, we conclude by discussing the strategy of inferior species to survive and the mechanism of uniform persistence for the three species ecosystem.
Citation: Ting-Hui Yang, Weinian Zhang, Kaijen Cheng. Global dynamics of three species omnivory models with Lotka-Volterra interaction. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2867-2881. doi: 10.3934/dcdsb.2016077
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##### References:
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