Stability and bifurcation for a stochastic differential algebraic Holling-II predator-prey model with nonlinear harvesting and delay

In this paper, a stochastic delayed differential algebraic predator-prey model with Michaelis-Menten-type prey harvesting is proposed. Due to the influence of gestation delay and stochastic fluctuations, the proposed model displays a complex dynamics. Criteria on the local stability of the interior equilibrium are established, and the effect of gestation delay on the model dynamics is discussed. Taking the gestation delay and economic profit as bifurcation parameters, Hopf bifurcation and singularity induced bifurcation can occur as they cross through some critical values, respectively. Moreover, the solution of the model will blow up in a limited time when delay tau > tau(0). Then, we calculate the fluctuation intensity of the stochastic fluctuations by Fourier transform method, which is the key to illustrate the effect of stochastic fluctuations. Finally, we demonstrate our theoretical results by numerical simulations.