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<p>Three-dimensional predator-prey Lotka-Volterra systems with an identical intrinsic growth rate can have either one, or two, or three predator-prey interaction pairs. In the case with one pair, their global topological dynamics in the first octant of the compactified Poincaré ball have been characterized recently. Here we study the case with three pairs, and complete their classification on global dynamics: exactly 23 topologically distinct classes. Among which the <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\omega\)</EquationSource></InlineEquation>- and <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(\alpha\)</EquationSource></InlineEquation>-limit sets of any trajectory are either an equilibrium, or a periodic orbit, or a polygonal loop. Moreover, we show that every bounded predator-prey system (with one exception) admits a unique balance simplex. This geometric framework is helpful to characterize the global dynamics.</p>

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Global Dynamics of 3D Predator-Prey Lotka-Volterra System with the Identical Intrinsic Growth Rate. II: Three Predator-Prey Interaction Pairs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月29日

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  • Fengli Liang,
  • Jifa Jiang,
  • Xiang Zhang

摘要

Three-dimensional predator-prey Lotka-Volterra systems with an identical intrinsic growth rate can have either one, or two, or three predator-prey interaction pairs. In the case with one pair, their global topological dynamics in the first octant of the compactified Poincaré ball have been characterized recently. Here we study the case with three pairs, and complete their classification on global dynamics: exactly 23 topologically distinct classes. Among which the \(\omega\)- and \(\alpha\)-limit sets of any trajectory are either an equilibrium, or a periodic orbit, or a polygonal loop. Moreover, we show that every bounded predator-prey system (with one exception) admits a unique balance simplex. This geometric framework is helpful to characterize the global dynamics.