Dynamics of transitions in population interactions

A two-species model with transitions between population interactions is studied. Rich dynamics is observed as the number and quality of equilibria change when model parameters and functional responses vary. Existence and stability of equilibria and nonexistence 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 (mutualism, competition, host–parasite) between the species, and several numerical examples are provided to illustrate the main results in this work.