论文标题
Lotka的入侵图的结构稳定性 - 沃特拉系统
Structural stability of invasion graphs for Lotka--Volterra systems
论文作者
论文摘要
在本文中，我们详细研究了Lotka（volterra with volterra-volterra-lyapunov稳定结构矩阵）的全球吸引子的结构。我们考虑了[19]中最近引入的入侵图，并证明其边缘代表了系统平衡之间的所有杂斜联连接。我们还研究了该结构在问题参数的扰动方面的稳定性。这使我们能够与经典的数学概念相干地引入生态学结构稳定性的定义，在该概念中，存在详细的几何结构，在扰动下稳健，该结构控制了瞬态和渐近动力学。
In this paper, we study in detail the structure of the global attractor for the Lotka--Volterra system with a Volterra--Lyapunov stable structural matrix. We consider the invasion graph as recently introduced in [19] and prove that its edges represent all the heteroclinic connections between the equilibria of the system. We also study the stability of this structure with respect to the perturbation of the problem parameters. This allows us to introduce a definition of structural stability in ecology in coherence with the classical mathematical concept where there exists a detailed geometrical structure, robust under perturbation, that governs the transient and asymptotic dynamics.
