A bioeconomic differential algebraic predator-prey model with nonlinear prey harvesting

In this paper, we propose a bioeconomic differential algebraic predator-prey model with Holling type II functional response and nonlinear prey harvesting. As the nonlinear prey harvesting is introduced, the proposed model displays a complex dynamics in the predator-prey plane. Taking into account of the economic factor, our predator-prey system is established by bioeconomic differential algebraic equations. The effect of economic profit on the proposed model is analyzed by viewing it as a bifurcation parameter. By jointly using the normal form of differential algebraic models and the bifurcation theory, the stability and bifurcations (singularity induced bifurcation, Hopf bifurcation) are discussed. These results obtained here reveal richer dynamics of the bioeconomic differential algebraic predator-prey model with nonlinear prey harvesting, and suggest a guidance for harvesting in the practical word. Finally, numerical simulations are given to demonstrate the results.