Deterministic and Stochastic Research of Cubic Population Model with Harvesting

Gültekin Ö., Eskin Ç., Yazicioǧlu E.

Fluctuation and Noise Letters, vol.20, no.3, 2021 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.1142/s0219477521500231
  • Journal Name: Fluctuation and Noise Letters
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Allee effect, Fokker Planck equation, harvesting, population model, Gaussian white noise, Gaussian colored noise, EXTINCTION RISK, NOISE COLOR, ALLEE, DYNAMICS, PREDATOR, DRIVEN, FERTILIZATION, SYSTEM
  • Middle East Technical University Affiliated: Yes


© 2021 World Scientific Publishing Company.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 are 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.