Global dynamics of a Lotka–Volterra system in ℝ³

Abstract

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.

Keywords:

• Lotka–Volterra system
• phase portraits
• Poincaré ball

2000 Mathematics Subject Classification:

• 37C10
• 34C05