Phase portraits of a family of Kolmogorov systems depending on six parameters
| dc.contributor.author | Diz-Pita, Erika | |
| dc.contributor.author | Llibre, Jaume | |
| dc.contributor.author | Otero-Espinar, M. Victoria | |
| dc.date.accessioned | 2021-08-23T19:48:39Z | |
| dc.date.available | 2021-08-23T19:48:39Z | |
| dc.date.issued | 2021-05-03 | |
| 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.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 38 pages | |
| dc.format.medium | 1 file (.pdf) | |
| 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. <i>Electronic Journal of Differential Equations, 2021</i>(35), pp. 1-38. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14432 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Kolmogorov system | |
| dc.subject | Lotka-Volterra system | |
| dc.subject | Phase portrait | |
| dc.subject | Poincare disc | |
| dc.title | Phase portraits of a family of Kolmogorov systems depending on six parameters | en_US |
| dc.type | Article |