论文标题
通过资源竞争，许多物种的动态
Dynamics of many species through competition for resources
论文作者
论文摘要
本文关注的是，物种消耗非相互作用资源的资源竞争模型。这种微分方程的系统是通过在平衡处重新归一化的麦克阿瑟竞争模型来正式获得的，并同意由Mirrahimi S，Perthame B，Wakano JY研究的性状连续模型[J. [J.数学。生物。 64（7）：1189-1223，2012]。作为一个动态系统，发生自组织的不同物种的产生。给出了生存的必要条件。我们通过优化问题证明了进化稳定分布（ESD）的存在，并提出了一种独立的算法来直接计算ESD。在某些结构条件下，随着时间的发展，系统的解决方案被证明可以接近离散的ESD。事实证明，系统的时间离散化满足了两种所需的特性：阳性和能量耗散。给出数值示例以说明某些有趣的生物学现象。
This paper is concerned with a mathematical model of competition for resource where species consume noninteracting resources. This system of differential equations is formally obtained by renormalizing the MacArthur's competition model at equilibrium, and agrees with the trait-continuous model studied by Mirrahimi S, Perthame B, Wakano JY [J. Math. Biol. 64(7): 1189-1223, 2012]. As a dynamical system, self-organized generation of distinct species occurs. The necessary conditions for survival are given. We prove the existence of the evolutionary stable distribution (ESD) through an optimization problem and present an independent algorithm to compute the ESD directly. Under certain structural conditions, solutions of the system are shown to approach the discrete ESD as time evolves. The time discretization of the system is proven to satisfy two desired properties: positivity and energy dissipation. Numerical examples are given to illustrate certain interesting biological phenomena.
