We address the biological dynamics problem of the persistence of several species in conditions of non-existence of an equilibrium, including an example of stabilization by predation and the very controversial “competitive exclusion” (which depends on the precise definition of persistence). We give normal forms for various examples of such (essentially dynamical) persistence and comments on the involved topology, which implies the presence of exceptional heteroclinic connections binding equilibria on the boundary.

中文翻译：

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多样性动态保存的新方案：稳定性和拓扑结构的评论

我们解决了几个物种在不存在平衡的条件下持续存在的生物动力学问题，包括一个通过捕食稳定的例子和非常有争议的“竞争排斥”（这取决于持续性的精确定义）。我们给出了这种（基本上是动态的）持久性的各种例子的范式，并对所涉及的拓扑进行了评论，这意味着在边界上存在结合平衡的特殊异宿连接。