Phase portraits of a family of Kolmogorov systems depending on six parameters
| dc.contributor.author | Diz-Pita, Erika (  0000-0002-7086-6614 ) | |
| dc.contributor.author | Llibre, Jaume ( 0000-0002-9511-5999 ) | |
| dc.contributor.author | Otero-Espinar, M. Victoria ( 0000-0002-0201-0523 ) | |
| dc.date.accessioned | 2021-08-23T19:48:39Z | |
| dc.date.available | 2021-08-23T19:48:39Z | |
| dc.date.issued | 2021-05-03 | |
| dc.identifier.citation | Diz-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 |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://digital.library.txstate.edu/handle/10877/14432 | |
| dc.description.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. | |
| dc.format | Text | |
| dc.format.extent | 38 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.language.iso | en | en_US |
| dc.publisher | Texas State University, Department of Mathematics | en_US |
| dc.source | Electronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Kolmogorov system | en_US |
| dc.subject | Lotka-Volterra system | en_US |
| dc.subject | Phase portrait | en_US |
| dc.subject | Poincare disc | en_US |
| dc.title | Phase portraits of a family of Kolmogorov systems depending on six parameters | en_US |
| dc.type | publishedVersion | |
| txstate.documenttype | Article | |
| dc.rights.license |  This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.description.department | Mathematics |
