ANALISIS KESTABILAN MODEL PREDATOR PREY DENGAN TINGKATAN USIA PADA DUA PREY DAN DUA PREDATOR DENGAN FUNGSI RESPON MONOD HALDANE DAN KANIBALISME

Robiatul Witari Wilda; Dita Monita; Febrianto Afli; Ahmad Muammar Kadafi

doi:10.20527/epsilon.v17i2.10685

ANALISIS KESTABILAN MODEL PREDATOR PREY DENGAN TINGKATAN USIA PADA DUA PREY DAN DUA PREDATOR DENGAN FUNGSI RESPON MONOD HALDANE DAN KANIBALISME

Robiatul Witari Wilda, Dita Monita, Febrianto Afli, Ahmad Muammar Kadafi

Abstract

This paper discusses a predator-prey stage structure model for two predators and two preys with Monod Haldane and cannibalism response functions that describe the interactions between populations of young prey, adult prey, young predator, and adult predator. In this model it is assumed that only adult predators are capable of attacking to consume young predators, only adult prey are capable of reproduction, there is a Monod-Haldane effect describing the phenomenon of group defense where predation is reduced, or even prevented altogether, because the ability increases from prey for further defense or camouflage when their numbers are large enough. Dynamic analysis is carried out by determining the equilibrium point and its existence conditions and analyzing the local stability of the equilibrium point. The predator-prey model has three equilibrium points, namely the trivial equilibrium point, the prey free equilibrium point and an interior point that exists under certain conditions. The equilibrium points is locally asymptotically stable under certain conditions. The results of the numerical simulations show suitability with the results of dynamic analysis.

Keywords

prey-predator model, stage structure, Monod Haldane, cannibalism, stability analysis

Full Text:

PDF

References

Amalia, D. dan Savitri, D. (2023). Analisis Dinamik Model Predator-Prey

dengan Fungsi Respon Monod Haldane. MATHunesa: Jurnal Ilmiah Matematika, vol. 11, no. 2, pp. 287–294, Aug., doi: 10.26740/mathunesa.v11n2.p287-294.

Anton, H. (1997). Elementary Linear Algebra. New York: John Wiley.

Boyce, W. E., dan DiPrima, R. C. (2012). Elementary Differential Equations and Boundary Value Problems.

Gaib, M. B. dan Ja’a, W. At. (2020). Analisis Kestabilan Model Interaksi Predator-Prey Dengan Fungsi Respon Monod-Haldane Dan Perilaku Anti Pemangsa. Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi, vol. 8, no. 2, pp. 51–59, Dec. 2020, doi: 10.34312/euler.v8i2.10407.

Hidayati, S. N. (2020). Analisis Dinamik Model Matematika Predator-Prey Akibat Rasa Takut dan Pertahanan Kelompok. Tesis, Universitas Islam Negeri Maulana Malik Ibrahim, Malang.

Holling, C. S. (1959). Some Characteristics of Simple Types of Predation and Parasitism. The Canadian Entomologist, 91(7), 385–398.

Mortoja, S. G., Panja, P. dan Mondal, S. K. (2018). Dynamics of a predator-prey model with stage-structure on both species and anti-predator behavior. Inform Med Unlocked, vol. 10, pp. 50–57. doi: 10.1016/J.IMU.2017.12.004.

Perko. (2001). Linear Systems. Differential Equations and Dynamical Systems, (hal. 1–63).

Susanto, H. (2021). Potret dan Rencana Pengelolaan Ekosistem Karst Kalimantan. Pusat Pengendalian Pembangunan Ekoregion Kalimantan Kementerian Lingkungan Hidup dan Kehutanan. Accessed: Oct. 19, 2023. [Online]. Available: https://p3ekalimantan.menlhk.go.id/wp-content/uploads/2021/11/Potret-dan-Rencana-Pengelolaan-Ekosistem-Karst-Kalimantan.pdf

Widowati, S. dan Sutimin, S. (2007). Buku Ajar Pemodelan Matematika. Semarang: Jurusan Matematika UNDIP.

Zhang, F., Chen,Y., and Li, J. (2019). Dynamical analysis of a stage-structured predator-prey model with cannibalism. Math Biosci, vol. 307, pp. 33–41, Jan. 2019, doi: 10.1016/J.MBS.2018.11.004.

Zhang,L. and Zhang, C. (2010). Rich Dynamic of A Stage-Structured Prey–Predator Model with Cannibalism and Periodic Attacking Rate. Commun Nonlinear Sci Numer Simul, vol. 15, no. 12, pp. 4029–4040. doi: 10.1016/J.CNSNS.2010.02.009.

DOI: https://doi.org/10.20527/epsilon.v17i2.10685