报告题目：Global Dynamics and Traveling Wave Solutions of Three Species Omnivory Models with Lotka-Volterra Interaction

报告人：杨定挥 教授（淡江大学数学系）

报告时间： 2016 年11 月11，下午3点

报告地点 ：数学实验室

摘要： In this work, we consider the community of diffusive/non-diffusive 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). Without diffusion, we can completely classify all dynamics of the model corresponding all parameters with a mild biological restriction. All local dynamics and most parts of global dynamics are established corresponding to the classification. Moreover, the whole is uniformly persistent when 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.

The part with diffusion of this work is to investigate the existence and non-existence of traveling wave solutions for this model. The minimal speed c* of traveling wave solutions of the model is characterized. If the wave speed is greater than or equal to c*, we show the existence of traveling wave solutions connecting trivial and positive equilibria by combining the upper and lower solutions with the contracting rectangle. On the other hand, if the wave speed is less than c*, the non-existence of such solutions is also established. Finally, corresponding to our theoretical results some numerical simulations are performed and biological meanings are interpreted.

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注：本次讲座将纳入数学系继续教育课程。

理学院

2016年11月7日