Global dynamics of a classical Lotka-Volterra competition-diffusion-advection system
Global dynamics of a classical Lotka-Volterra competition-diffusion-advection system
复制标题
经典 Lotka-Volterra 竞争-扩散-平流系统的全局动力学
DOI：
10.1016/j.jfa.2018.03.006
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发表时间：
2018
影响因子：
1.7
通讯作者：
Xiao Dongmei
中科院分区：
文献类型：
--
作者：
Zhou Peng;Xiao Dongmei
本文研究了一个经典的两种群Lotka-Volterra竞争扩散平流系统，其中两个竞争者的扩散速率和平流率是成比例的。利用主谱理论，我们首先建立了共存(正)定态的一个关键的先验估计，这是联系局部和全局动力学的有力工具。然后，我们借助单调动力系统理论，进一步对所有可能的长时间动力学行为进行了完整的分类。最后，我们将这些结果应用于两个种群竞争相同资源的特殊情况，得到了关于所有类型的全局动力的某些可变参数的精确准则。这项工作肯定地回答了Lou等人的猜想。在[34]中，通过考虑在一定条件下更一般的模型，也可以看作是He和Ni[19]对竞争扩散系统的进一步发展，其中我们在论证中引入了新的成分，以克服平流的影响所造成的困难。
In this paper, we study a classical two species Lotka–Volterra competition–diffusion–advection system, where the diffusion and advection rates of two competitors are supposed to be proportional. By employing the principal spectral theory, we first establish a key a priori estimate on the co-existence (positive) steady state, which is a powerful tool to link the local and global dynamics. We then further present a complete classification on all possible long-time dynamical behaviors by appealing to the theory of monotone dynamical systems. Lastly, we apply these results to a special situation where two species are competing for the same resources and obtain a sharp criteria in term of certain variable parameters for all kinds of global dynamics. This work gives a positive answer to the conjecture proposed by Lou et al. in [34] by considering a more general model under certain conditions, and also, can be seen as a further development of He and Ni [19] for competition–diffusion system, where we bring new ingredients in the arguments to overcome the difficulty caused by the involvement of advection.