School of Mathematics and Information Technology, Yuncheng University, Yuncheng, Shanxi, 044000, China.
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada.
Math Biosci Eng. 2019 Mar 27;16(4):2697-2716. doi: 10.3934/mbe.2019134.
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.
在本文中，我们研究了斑块环境下的两种竞争模型。假设其中一个物种在斑块之间随机扩散，具有恒定的扩散延迟。我们表明，在任意数量的斑块的两种配置（完全连接配置和环形结构配置）中，扩散不会影响均匀共存平衡点的稳定性和不稳定性。对于弱竞争情况，我们表明均匀共存平衡点是唯一的共存平衡点，两种物种都可以共存。然而，对于强竞争情况，我们表明均匀共存平衡点是不稳定的，此外，小的扩散率可以诱导多个共存平衡点，并且扩散（包括扩散率和扩散延迟）确实对确定竞争结果有影响，并可以诱导多稳定性。因此，两种物种的瞬态共存可以在所有斑块中观察到，尽管不是在所有斑块中，但长期共存是可能的。
