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.