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The impacts of dispersal on the competition outcome of multi-patch competition models

1 School of Mathematics and Information Technology, Yuncheng University, Yuncheng, Shanxi, 044000, China
2 Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

Special Issues: Recent Advances in Mathematical Population Dynamics

In this paper, we study a two-species competition model over patchy environments. One species is assumed to disperse randomly between patches with a constant dispersal delay. We show that the dispersal does not affect the stability and instability of the homogeneous coexistence equilibrium in two configurations (fully connected configuration and ring-structured configuration) of an arbitrary number of patches. For the weak competition case, we show that the homogeneous coexistence equilibrium is the unique coexistence equilibrium and both species can coexist. However, for the strong competition case, we show that the homogeneous coexistence equilibrium is unstable, in addition, small dispersal rate can induce multiple coexistence equilibria and the dispersal (including the dispersal rate and the dispersal delay) does have impacts on determining the competition outcome and can induce multi-stability. As a result, transient coexistence of both species can be observed in all patches, and long-term coexistence of both species in some patches, though not in all patches, becomes possible.
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Keywords dispersal; stability; patch; weak competition; strong competition

Citation: Ali Mai, Guowei Sun, LinWang. The impacts of dispersal on the competition outcome of multi-patch competition models. Mathematical Biosciences and Engineering, 2019, 16(4): 2697-2716. doi: 10.3934/mbe.2019134

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