Global Dynamics of 3D Type-K Competitive Lotka-Volterra System with the Identical Intrinsic Growth Rate

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发表日期：

2025年5月20日

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Fengli Liang,
Jifa Jiang,
Xiang Zhang

摘要

For the three-dimensional type-K competitive Lotka-Volterra system with the identical intrinsic growth rate, we completely characterize its global dynamics in the Poincaré compactification of the system in the positive octant of $\mathbb {R}^{3}$ $R^{3}$ . Precisely, with the help of the replicator equations it is proved that this kind of system can have exactly 44 topologically different phase portraits. As a consequence, we obtain the necessary and sufficient conditions for the system to be bounded in the positive octant and verify that the $\alpha $ $α$ and $\omega $ $ω$ limit sets of any orbit of the compactified vector field associated to the system are both equilibria.