A Predator-Prey Model with Fear Factor, Allee Effect and Periodic Harvesting
- 27 Downloads
A two-dimensional predator-prey model constructed in this article to study how the fear of predator on prey will reduce the intrinsic growth rate of prey. The Allee effect in prey population is included to describe the minimum requirement of the individual to achieve the positive growth of the prey population. Anti-predation and harvesting on the predator population are also considered in the model. We non-dimensionalized the model first before analyzing the existence and the local stability criteria of all equilibrium points. The analytical results showed how the harvesting intervention would determine the local stability criteria of the coexistence equilibrium point. We found that the time scale separation does not impact the stability of equilibrium points. Some numerical simulation is given to show how the system behaves depend on the periodic harvesting interventions.
KeywordsPredator Prey Allee effect Fear factor Anti-predation Periodic harvesting
We thank to all reviewers for their valuable comments. This research is funded by Universitas Indonesia with PITTA research grant Scheme, 2019 (ID number: NKB-0627/UN2.R3.1/HKP.05.00/2019).
- 3.Putri, A., Aldila, D.: Prey-predator interaction model between herring and seals with phocine distemper virus (PDV) infection in seals. In: AIP Conference Proceedings 2023, vol. 020239 (2018). https://doi.org/10.1063/1.5064236
- 4.Triharyuni, S., Aldila, D.: A mathematical model of predator-prey interaction between seal-herring and steelhead trout. In: AIP Conference Proceedings 1862, vol. 030152 (2017). https://doi.org/10.1063/1.4991256
- 5.Sayekti, I.M., Malik, M., Aldila, D.: One-prey two-predator model with prey harvesting in a food chain interaction. In: AIP Conference Proceedings 1862, vol. 030124 (2017). https://doi.org/10.1063/1.4991228
- 10.Li, T., Huang, X., Xie, X.: Stability of a stage-structured predator-prey model with Allee effect and harvesting. Commun. Math. Biol. Neurosci. 2019, 13 (2019)Google Scholar