Firdiansyah, A. L., & Nurhidayati, N. (2021). Dynamics in two competing predators-one prey system with two types of Holling and fear effect. Jambura Journal of Biomathematics (JJBM), 2(2), 58–67. https://doi.org/10.34312/jjbm.v2i2.11264
Guin, L. N., Mandal, G., Mondal, M., & Chakravarty, S. (2022). A chaotic tri-trophic food chain model supplemented by Allee effect. International Journal of Dynamics and Control, 11(2), 528–554. https://doi.org/10.1007/s40435-022-01017-0
Huda, M. N., Trisilowati, T., & Suryanto, A. (2017). Dynamical Analysis of Fractional-Order Hastings-Powell Food Chain Model with Alternative Food. The Journal of Experimental Life Sciences, 7(1), 39–44. https://doi.org/10.21776/ub.jels.2016.007.01.08
Ibrahim, R., Yahya, L., Rahmi, E., & Resmawan, R. (2021). Analisis dinamik model predator-prey tipe Gause dengan wabah penyakit pada prey. Jambura Journal of Biomathematics (JJBM), 2(1), 20–28. https://doi.org/10.34312/jjbm.v2i1.10363
Ma, R., Bai, Y., & Wang, F. (2020). Dynamical behavior analysis of a two-dimensional discrete predator-prey model with prey refuge and fear factor. Journal of Applied Analysis and Computation, 10(4), 1683–1697. https://doi.org/10.11948/20190426
Mahapatra, G. S., Santra, P. K., & Bonyah, E. (2021). Dynamics on Effect of Prey Refuge Proportional to Predator in Discrete-Time Prey-Predator Model. Complexity, 2021. https://doi.org/10.1155/2021/6209908
Mandal, S., Al Basir, F., & Ray, S. (2021). Additive Allee effect of top predator in a mathematical model of three species food chain. Energy, Ecology and Environment, 6(5), 451–461. https://doi.org/10.1007/s40974-020-00200-3
Molla, H., Sarwardi, S., Smith, S. R., & Haque, M. (2022). Dynamics of adding variable prey refuge and an Allee effect to a predator–prey model. Alexandria Engineering Journal, 61(6), 4175–4188. https://doi.org/10.1016/j.aej.2021.09.039
Mukherjee, D., & Maji, C. (2020). Bifurcation analysis of a Holling type II predator-prey model with refuge. Chinese Journal of Physics, 65(August 2019), 153–162. https://doi.org/10.1016/j.cjph.2020.02.012
Nath, B., Kumari, N., Kumar, V., & Das, K. P. (2022). Refugia and Allee Effect in Prey Species Stabilize Chaos in a Tri-Trophic Food Chain Model. Differential Equations and Dynamical Systems, 30(3), 631–657. https://doi.org/10.1007/s12591-019-00457-z
Pal, N., Samanta, S., & Rana, S. (2017). The Impact of Constant Immigration on a Tri-trophic Food Chain Model. International Journal of Applied and Computational Mathematics, 3(4), 3615–3644. https://doi.org/10.1007/s40819-017-0317-5
Panja, P., Gayen, S., Kar, T., & Jana, D. K. (2022). Complex dynamics of a three species predator–prey model with two nonlinearly competing species. Results in Control and Optimization, 8(March), 100153. https://doi.org/10.1016/j.rico.2022.100153
Parshad, R. D., Quansah, E., Black, K., Upadhyay, R. K., Tiwari, S. K., & Kumari, N. (2016). Long time dynamics of a three-species food chain model with Allee effect in the top predator. Computers and Mathematics with Applications, 71(2), 503–528. https://doi.org/10.1016/j.camwa.2015.12.015
Savitri, D., & Panigoro, H. S. (2020). Bifurkasi Hopf pada model prey-predator-super predator dengan fungsi respon yang berbeda. Jambura Journal of Biomathematics (JJBM), 1(2), 65–70. https://doi.org/10.34312/jjbm.v1i2.8399
Thirthar, A. A., Majeed, S. J., Alqudah, M. A., Panja, P., & Abdeljawad, T. (2022). Fear effect in a predator-prey model with additional food, prey refuge and harvesting on super predator. Chaos, Solitons and Fractals, 159, 112091. https://doi.org/10.1016/j.chaos.2022.112091
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Affiliations
Haya Rohmatunnisa
Student
Tri Sri Noor Asih
Department of Mathematics, Universitas Negeri Semarang
Stevanus Budi Waluya
Mathematics Department, Universitas Negeri Semarang
Muhammad Fajar Safaatullah
Mathematics Department, Universitas Negeri Semarang
The influence of Allee effect, refugia, and alternative food on a three-species predator-prey model
Vol 12 No 2 (2023): Unnes Journal of Mathematics
Submitted: Dec 1, 2023
Published: Jun 3, 2024
Abstract
This research presents a mathematical model for a three-species predator-prey system, incorporating the Allee effect, refugia, and alternative food. The interactions between prey and intermediate predator, as well as intermediate predator and top predator, are modeled using Holling type II response functions. The resulting system of nonlinear equations yields four equilibrium points, one unstable and three stable locally. Analytical calculations indicate that refugia and alternative food minimally affect the top predator's population growth, while the Allee effect influences the growth of prey and intermediate predator populations. Numerical simulations further support these findings, highlighting the nuanced impacts of these factors on the dynamics of the three-species system.