Bifurcations and periodic orbits in variable population interactions (Q1951466)

A two-specie interaction model with harvest on one of the species is studied, where the harvesting function is of saturation type and the linear \(\alpha\)-functions represents the variable interactions; mutualism, competition, host-parasite between the species are incorporated. Existence and stability of equilibria and existence of periodic solutions are established, existence of some bifurcation phenomena are analytically and numerically studied, explicit threshold values are computed to determine the kind of interaction between the species, and center-type equilibria, Hopf bifurcations and periodic solutions are found for the first time in this kind of models.