Bistability of a two-species competition model with stage structure

Abstract

In this paper, we focus on the dynamic behaviors of the bistability for a two-species Lotka–Volterra competition model with stage structure. Using the theory of generalized saddle-point behaviors, it is shown that there exists a [Formula: see text]-separatrix [Formula: see text] on its state space such that Species 2 wins the competition whenever the initial distribution is above [Formula: see text], while Species 1 wins the competition whenever the initial distribution is below [Formula: see text]. Combining with the previous conclusions of the system, we give a complete classification for global competitive dynamics. Furthermore, we carefully analyze the changes of the competition outcome after introducing the stage structure. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.