Stability and bifurcation analysis of two-species competitive model with Michaelis–Menten type harvesting in the first species

Abstract

Abstract In this paper, a two-species competitive model with Michaelis–Menten type harvesting in the first species is studied. We have made a detailed mathematical analysis of the model to describe some important results that may be produced by the interaction of biological resources. The permanence, stability, and bifurcation (saddle-node bifurcation and transcritical bifurcation) of the model are investigated. The results show that with the change of parameters, two species could eventually coexist, become extinct or one species will be driven to extinction and the other species will coexist. Moreover, by constructing the Lyapunov function, sufficient conditions to ensure the global asymptotic stability of the positive equilibrium are given. Our study shows that compared with linear harvesting, nonlinear harvesting can exhibit more complex dynamic behavior. Numerical simulations are presented to illustrate the theoretical results.

Keywords

• Competitive
• Michaelis–Menten type harvesting
• Stability
• Bifurcation