The Dynamics of a Bioeconomic Model with Michaelis–Menten Type Prey Harvesting

In this paper, we propose a bioeconomic predator–prey model with Michaelis–Menten type prey harvesting and general functional response which is described by a differential–algebraic system. Using the local parameterization, we derive an equivalent parametric system and investigate its dynamics in terms of local stability and Hopf bifurcation. The economic profit is chosen as a bifurcation parameter to prove the occurrence of Hopf bifurcation phenomenon in the neighborhood of the interior equilibrium. Moreover, we calculate the first Lyapunov coefficient to study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions based on the normal form theory. Numerical simulations are carried out to demonstrate the analytical results.