Stability analysis of a two-species model with transitions between population interactions

Stability of a simple two-species system is investigated. This model assumes that the kind of inter-specific interactions is not fixed, and that it depends on the system state, i.e., undergoes transitions between different population interactions due to variation in population densities. The main goal is to show the effects of the transitions between different population interactions on the two-species coexistence, and on the stability conditions of multiple equilibria.