Abstract
In this paper, a study of Michaelis–Menten type harvesting effects on a population with outbreak characteristic in stochastic environment is done formulating stochastic model. The Ludwig model (Ludwig et al., 1978) is chosen as the base mathematical model for the population. Steady state probability distribution and stationary potential function of the population are determined. P-bifurcation analysis has been presented. The impact of the noises and cross correlations strength on outbreak and extinction of the population are measured numerically using probability. It is observed that random rate of Michaelis–Menten type harvesting may extinct the population. The choice of noise or type of harvesting process to population control cannot be uniquely defined and deeply depends on the exogenous factors (extrinsic and intrinsic noise), a contradiction to the earlier reports. Various complex ecological phenomena like noise enhance stability, phase regime shift, etc., are identified in the system.
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