Dynamics of a Discrete Two-Species Competitive Model with Michaelies-Menten Type Harvesting in the First Species (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we use a semidiscretization method to derive a discrete two-species competitive model with Michaelis-Menten type harvesting inthe first species. First, the existence and local stability of fixed points of thesystem are investigated by employing a key lemma. Subsequently, the transcritical bifurcation, period-doubling bifurcation and pitchfork bifurcation ofthe model are investigated by using the Center Manifold Theorem and bifurcation theory. Finally, numerical simulations are presented to illustratecorresponding theoretical results.
Keywords: Competitive model with Michaelis-Menten type harvesting; semidiscretization method; transcritical bifurcation; period-doubling bifurcation; pitchfork bifurcation.