Phase portraits of a family of Kolmogorov systems depending on six parameters
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We consider a general 3-dimensional Lotka-Volterra system with a rational first integral of degree two of the form H = xi yj zk. The restriction of this Lotka-Volterra system to each surface H(x, y, z) = h varying h ∈ ℝ provide Kolmogorov systems. With the additional assumption that they have a Darboux invariant of the form xℓ ym est they reduce to the Kolmogorov systems ẋ = x(α0 - μ(c1x + c2z2 + c3z)), z = z(c0 + c1x + c2z2 + c3z). We classify the phase portraits in the Poincaré disc of all these Kolmogorov systems which depend on six parameters.
CitationDiz-Pita, É., Llibre, J., & Otero-Espinar, M. V. (2021). Phase portraits of a family of Kolmogorov systems depending on six parameters. Electronic Journal of Differential Equations, 2021(35), pp. 1-38.
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