Stability Analysis of a Predator-prey Model with Anti-Predator Behavior and Allee Effect on Prey
DOI:
https://doi.org/10.29303/emj.v6i2.191Keywords:
Predator-Prey, Allee Effect, Anti Predator, Runge-KuttaAbstract
We explore a predator-prey model that incorporates both anti-predator behavior by the prey and the Allee effect, where population growth declines at low densities. Four equilibrium points emerge: extinction for both species (E0), two predator extinction points (E1 and E2), and one coexistence point for both populations (E3). While the stability of E0, E2, and E3 depends on the given parameters, E1 is always unstable. We then verified this analysis through numerical simulations using Runge-Kutta method in Python.References
M. Putra, A. J. Dwi dan A. I. A Himayati. Stability Analysis of Leslie-Gower Model with Herd Behavior on Prey. Indonesia Journal of Pure and Applied Mathematics. 2022. Vol 4. No. 1, 65-71.
M. Putra, A.J. Dwi, A. Suryanto dan N. Shofianah. Stability analysis and Hopf bifurcation of intraguild predation model with Holling type II functional response. Int. J. Ecol. Dev. 32 (2017), no. 4, 110–118.
Ye, Y. , Hua Liu, Yumei Wei, Kai Zhang, MingMa dan Jianhua Ye. Dynamic study of a predator-prey model with Allee effect and Holling type-I functional response. Advances in Difference Equations. 2019. 2019-369.
Saadah, S., Abadi dan Dian Savitri. Model Interaksi Mangsa Pemangsa dengan Fungsi Respon Rasio Dependent Holling Tipe II dan Perilaku Anti Pemangsa. Jurnal Ilmiah Matematika. 2019. Vol 7. No. 2.
Indrajaya, D.; Suryanto, A.; Alghofari, A.R. Dynamics of modified Leslie-Gower predator-prey model with Beddington-DeAngelis functional response and additive Allee effect. Int. J. Ecol. Dev. 2016, 31, 60–71.
Yang, R., Xiao Zhao dan Yong An. Dynamical Analysis of a Delayed Diffusive Predator–Prey Model with Additional Food Provided and Anti-Predator Behavior. Mathematics. 2022, 10, 469.
Gaib, M. B. dan Wahdania At. Ja’a. Analisis Kestabilan Model Interaksi Predator-prey dengan Fungsi Respon Monod-Haldane dan Perilaku Anti Predator. Euler: Jurnal Ilmiah Matematika, Sains dan Teknologi. 2020. Vol. 8, No. 2, 51-59.
Suryanto, A. Isnani Darti, dan Syaiful Anam. Stability Analysis of a Fractional Order Modified Leslie-Gower Model with Additive Allee Effect. International Journal of Mathematics and Mathematical Sciences. Vol. 2017.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
All articles published in the Eigen Mathematics Journal will be available for free reading and downloading. The license applied to this journal is Creative Commons Attribution-Non-Commercial-Share Alike (CC BY-NC-SA).
