Bifurcation Analysis of a Discrete Amensalism Model

Abstract

By using model discretization of the piecewise constant argument method, a discrete amensalism model with nonselective harvesting and Allee effect is formulated. The dynamic analysis of the model is studied and the existence and stability of the equilibrium point are discussed. The fold bifurcation and flip bifurcation at the equilibrium point of the system are proved by using the bifurcation theory and the center manifold theorem. In order to control flip bifurcation and restore the system to a stable state, a hybrid control strategy of parameter perturbation and state feedback is adopted. Finally, the effectiveness of the theoretical results and the control strategy is verified by numerical simulations.