RT Journal Article
T1 Phase portraits of a family of Kolmogorov systems depending on six parameters
A1 Jaume Llibre, 
A1 Diz Pita, Erika
A1 Otero Espinar, María Victoria
AB 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. 
PB Department of Mathematics, Texas State University
YR 2021
FD 2021
LK https://hdl.handle.net/10347/39015
UL https://hdl.handle.net/10347/39015
LA eng
NO 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.
DS Minerva
RD 26 abr 2026