arXiv subjects

M. Victoria Otero-Espinar

Publications and source records attributed to M. Victoria Otero-Espinar.

3 recordsLinked to original sources

arXiv2025

Predator-prey models: a review on some recent adaptations

In the last years, predator-prey systems have increased their applications and have given rise to systems which represent more accurately different biological issues that appear in the context of interacting species. Our aim in this paper is to give a state-of-art review of recent predator-prey models which include some interesting characteristics as Allee effect, fear effect, cannibalism and immigration. We compare the qualitative results obtained for each of them, particularly regarding the equilibria, local and global stability, and the existence of limit cycles.

math.DS↗

arXiv2025

Planar Kolmogorov systems with infinitely many singular points at infinity

We classify the global dynamics of the five-parameter family of planar Kolmogorov systems \begin{equation*} \begin{split} \dot{y}&=y \left( b_0+ b_1 y z + b_2 y + b_3 z\right), \dot{z}&=z\left( c_0 + b_1 y z + b_2 y + b_3 z\right), \end{split} \end{equation*} which is obtained from the Lotka-Volterra systems of dimension three. These systems have infinitely many singular points at inifnity. We give the topological classification of their phase portraits in the Poincaré disc, so we can describe the dynamics of these systems near infinity. We prove that these systems have 13 topologically distinct global phase portraits.

math.DS↗

arXiv2025

Phase portraits of a family of Kolmogorov systems depending on six parameters

Consider a general $3$-dimensional Lotka-Volterra system with a rational first integral of degree two of the form $H=x^i y^j z^k$. The restriction of this Lotka-Volterra system to each surface $H(x,y,z)=h$ varying $h\in \mathbb{R}$ provide Kolmogorov systems. With the additional assumption that they have a Darboux invariant of the form $x^\ell y^m e^{st}$ they reduce to the Kolmogorov systems \begin{equation*} \begin{split} \dot{x}&=x \left( a_0- μ(c_1 x + c_2 z^2 + c_3 z)\right),\\ \dot{z}&=z\left( c_0+ c_1 x + c_2 z^2 + c_3 z\right). \end{split} \end{equation*} In this paper we classify the phase portraits in the Poincaré disc of all these Kolmogorov systems which depend on six parameters.

math.DS↗