Complex dynamics in a singular Leslie–Gower predator–prey bioeconomic model with time delay and stochastic fluctuations

In this paper, a class of singular Leslie–Gower predator–prey bioeconomic models with environment fluctuations and time delays is investigated. Local stability analysis of the model reveals that there is a phenomenon of singularity induced bifurcation due to variation of economic interest of harvesting. By choosing the delay as a bifurcation parameter, it is shown that the Hopf bifurcations can occur as the delay crosses some critical values. Then, the effect of a fluctuating environment on the singular stochastic delayed predator–prey bioeconomic model is discussed. Finally numerical simulations demonstrate that the amplitude of oscillation for population is enhanced when compared with the oscillation observed in the deterministic environment.