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dc.contributor.authorDiz-Pita, Erika ( Orcid Icon 0000-0002-7086-6614 )
dc.contributor.authorLlibre, Jaume ( Orcid Icon 0000-0002-9511-5999 )
dc.contributor.authorOtero-Espinar, M. Victoria ( Orcid Icon 0000-0002-0201-0523 )
dc.identifier.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.en_US

We consider a general 3-dimensional Lotka-Volterra system with a rational first integral of degree two of the form H = xiyjzk. 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 teh form xymest they reduce to the Kolmogorov systems

ẋ = x(α0 - μ(c1x + c2z2 + c3z)),
ż = z(c0 + c1x + c2z2 + c3z).

We classify the phase portraits in the Poincaré disc of all these Kolmogorov systems which depend on six parameters.

dc.format.extent38 pages
dc.format.medium1 file (.pdf)
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectKolmogorov systemen_US
dc.subjectLotka-Volterra systemen_US
dc.subjectPhase portraiten_US
dc.subjectPoincare discen_US
dc.titlePhase portraits of a family of Kolmogorov systems depending on six parametersen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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