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- and intra-gender competitions, fertility rates and a mating function. 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 median number of female sexual partners of each male for the conservation of a two-sex species.
nonsmooth ordinary differential equations
Mathematics Subject Classification 2010 (MSC 2010):
34C60; 37C10; 37N25; 92D25