Phase portraits of a family of Kolmogorov systems depending on six parameters
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Date
2021-05-03
Authors
Diz-Pita, Erika
Llibre, Jaume
Otero-Espinar, M. Victoria
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Kolmogorov system, Lotka-Volterra system, Phase portrait, Poincare disc
Citation
Diz-Pita, É., Llibre, J., & Otero-Espinar, M. V. (2021). Phase portraits of a family of Kolmogorov systems depending on six parameters. <i>Electronic Journal of Differential Equations, 2021</i>(35), pp. 1-38.
Rights
Attribution 4.0 International