Stability of steady state and boundedness of a 2-sex population model (Q1968655)

This study resumes/continues the author's previous concerns for establishing a realistic model, capable of rendering the contribution of both sexes to the reproduction process (on excluding monogamy or the dominance of either sex). The two essential concepts involved in the regulation of population(al) growth are boundedness and stability of equilibria. Once established the contributions brought by both sexes to the reproduction process, the author directs his researches towards the mode in which the demands of boundedness and/or stability affect the male and female species. The model employed for the ample demonstrations that follow is that of a heterosexual population, including three main classes: male, non-gestating female and gestating female, the first two classes being further sub-divided into pre-reproductive, reproductive and post-reproductive ones. Another section, entitled ``sufficient conditions for bounded populations'', tries to solve the following problem: how could the parameters be related if a population is not to exceed a pre-determined value, while the paragraph ``Sufficient conditions for asymptotic stability of a steady state'' analyses them in the idea that stability may assure populations' regulation.