Propagation dynamics of two species competition models in a periodic discrete habitat

Fan, Shiheng (2022) Propagation dynamics of two species competition models in a periodic discrete habitat. Masters thesis, Memorial University of Newfoundland.

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Abstract

Spreading speeds and traveling waves are essential in qualitative studying biological invasions. Sometimes, the invading species can lead to the extinction of the local species competing for resources, and such a phenomenon is called competition exclusion. In this thesis, we study the propagation dynamics of a Lotka-Volterra competition model in a periodic discrete habitat when competition exclusion occurs. First, we present general results on spreading speeds and traveling waves for monotone systems in a periodic discrete habitat. Under appropriate assumptions, we show that a semi-trivial equilibrium is globally stable for the spatially periodic initial value problem when competition exclusion happens. Then we establish the existence of the right ward spreading speed and its coincidence with the minimal wave speed for the spatially periodic right ward traveling waves. We obtain sufficient conditions for the linear determinacy of the right ward spreading speed. Ultimately, we apply all these results to a specific model and conduct numerical simulations to investigate the spreading of the two competing species in a periodic habitat.

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