In this work we consider the Lotka–Volterra system in ℝ3 introduced recently in [7], and studied also in [8] and [14]. In the first two papers the authors mainly studied the integrability of this differential system, while in the third paper they studied the system as a Hamilton- Poisson system, and also started the analysis of its dynamics. Here we provide the global phase portraits of this 3-dimensional Lotka–Volterra system in the Poincaré ball, that is in ℝ3 adding its extension to the infinity.

中文翻译：

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ℝ3 中 Lotka-Volterra 系统的全局动力学

在这项工作中，我们考虑了最近在 [7] 中介绍的ℝ3 中的 Lotka-Volterra 系统，并在 [8] 和 [14] 中进行了研究。在前两篇论文中，作者主要研究了这个微分系统的可积性，而在第三篇论文中，他们将该系统作为一个 Hamilton-Poisson 系统进行了研究，并开始了对其动力学的分析。在这里，我们提供了庞加莱球中这个 3 维 Lotka-Volterra 系统的全局相图，即在ℝ3 中将其扩展到无穷大。