Deterministic and Stochastic Research of Cubic Population Model with Harvesting

Abstract

A detailed examination of the effect of harvesting on a population has been carried out by extending the standard cubic deterministic model by considering a population under Allee effect with a quadratic function representing harvesting. Weak and strong Allee effect transitions, carrying capacity, and Allee threshold change according to harvesting is first discussed in the deterministic model. A Fokker Planck equation has been obtained starting from a Langevin equation subject to correlated Gaussian white noise with zero mean, and an Approximate Fokker Planck Equation has been obtained from a Langevin equation subject to correlated Gaussian colored noise with zero mean. This allowed to calculate the stationary probability distributions of populations, and thus to discuss the effects of linear and nonlinear (Holling type-II) harvesting for populations under Allee effect and subject to white and colored noises respectively.

18 pages, 33 figures

References in corpus (4)

• WKB theory of large deviations in stochastic populations
• Demographic stochasticity and extinction in populations with Allee effect
• Applications of WKB and Fokker-Planck methods in analyzing population extinction driven by weak demographic fluctuations
• Effect of Harvest on MTE Calculated by Single Step Process for Stochastic Population Model Under Allee Effect