A nonsmooth two-sex population model

TL;DR

This paper introduces a nonsmooth two-sex population model using coupled differential equations, analyzing its dynamics and equilibria based on parameters like sex ratio and mating behavior.

Contribution

It develops a novel nonsmooth two-sex population model and analyzes its equilibrium conditions and dynamics using geometrical techniques.

Findings

Identifies conditions for population equilibrium based on sex ratio.

Analyzes the influence of mating behavior on population stability.

Describes the role of parameters in the basin of attraction.

Abstract

This paper considers a two-dimensional logistic model to study populations with two genders. The growth behavior of a population is guided by two coupled ordinary differential equations given by a non-differentiable vector field whose parameters are the secondary sex ratio (the ratio of males to females at time of birth), inter-, intra- and outer-gender competitions, fertility and mortality rates and a mating function. For the case where there is no inter-gender competition and the mortality rates are negligible with respect to the density-dependent mortality, using geometrical techniques, we analyze the singularities and the basin of attraction of the system, determining the relationships between the parameters for which the system presents an equilibrium point. In particular, we describe conditions on the secondary sex ratio and discuss the role of the average number of female sexual partners of each male for the conservation of a two-sex species.