A nonsmooth two-sex population model.
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.
UNICAMP, Department of Mathematics, 13083-859 Campinas, SP, Brazil. Electronic address: garibaldi@ime.unicamp.br.
Eduardo
E
Garibaldi
UFSC, Department of Mathematics, 88040-900 Florianópolis, SC, Brazil. Electronic address: sobottka@mtm.ufsc.br.
Marcelo
M
Sobottka
D000818:Animals; D056808:Biostatistics; D005260:Female; D006801:Humans; D016015:Logistic Models; D008297:Male; D055641:Mathematical Concepts; D008954:Models, Biological; D011158:Population Growth; D012744:Sex Ratio
Geometric theory of differential equations; Mating function; Nonsmooth ordinary differential equations; Population dynamics; Two-sex models; Weak KAM theory