The role of correlation time in a stochastic population model with density-dependent harvesting

In this paper, a single-species stochastic population model is considered in the presence of density-dependent proportional harvesting. The stochastic model is considered to include the effects of fluctuation in the predation rate and environmental variability. Coloured cross-correlated Gaussian coloured noises are used to generate stochastic fluctuations. Steady-state probability distribution function and stationary potential are determined using the approximate Fokker–Planck equation. Phenomenological bifurcation analysis and mean first passage time have been computed. The average population density in the outbreak state is calculated using normalised probability distribution of the outbreak state. The species outbreak control strategy has been proposed. The key observations of this study are the negative cross-correlation strength-induced noise enhanced stability (NES) phenomenon and the environmental stochasticity-induced resonant activation (RA) phenomenon. Bistable to monostable phase regime shift is observed to depend on the environmental stochasticity whereas monostable to bistatble phase regime shift is observed to depend on correlation time of the environmental stochasticity.