Phase portraits of cubic polynomial Kolmogorov differential systems having a rational first integral of degree three

2025/05/01 by Jaume Llibre, Renhao Tian
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Quantum chaos and dynamical systems #Nonlinear Waves and Solitons

paper · doi:10.1063/5.0220041

Abstract

We classify all global phase portraits in the Poincaré disc of the cubic polynomial Kolmogorov differential systems having a well-defined rational first integral of degree three at the origin. For such differential systems there are exactly two different global phase portraits up to a reversal of the sense of their orbits.

Citations

• Global analytic first integrals for the real planar Lotka-Volterra system

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