[PDF][PDF] Phase portraits of a family of Kolmogorov systems depending on six parameters

E Diz-Pita, J Llibre, M Otero-Espinar - 2021 - digital.library.txstate.edu
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 …

Evolutionary stable strategies and cubic vector fields

J Bastos, C Buzzi, P Santana - Nonlinear Differential Equations and …, 2024 - Springer
The introduction of concepts of Game Theory and Ordinary Differential Equations into
Biology gave birth to the field of Evolutionary Stable Strategies, with applications in Biology …

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems

T Li, J Llibre - Expositiones Mathematicae, 2021 - Elsevier
Although planar quadratic differential systems and their applications have been studied in
more than one thousand papers, we still have no complete understanding of these systems …

[PDF][PDF] Quadratic systems with an invariant algebraic curve of degree 3 and a Darboux invariant

J Llibre, R Oliveira, CAB Rodrigues - 2021 - digital.library.txstate.edu
Let QS be the class of non-degenerate planar quadratic differential systems and QS3 its
subclass formed by the systems possessing an invariant cubic ƒ (x, y)= 0. In this article …

Exactly solvable quadratic differential equation systems through generalized inversion

Á Bácsi, AT Kocsis - Qualitative Theory of Dynamical Systems, 2023 - Springer
We study the autonomous systems of quadratic differential equations of the form x˙ i (t)= x (t)
TA ix (t)+ vi T x (t) with x (t)=(x 1 (t), x 2 (t),…, xi (t),⋯) which, in general, cannot be solved …