Analisis Dinamik Model Predator-Prey dengan Struktur Usia dan Perilaku Anti-Predator

Ainun Sukmawati Al Idrus; Ayub Prianto  Abd. Gani; Nurlaila  Zaid

doi:10.55657/rmns.v1i2.63

Authors

Ainun Sukmawati Al Idrus Program Studi Matematika, Universitas Negeri Gorontalo, Bone Bolango 96119, Indonesia
Ayub Prianto Abd. Gani Program Studi Matematika, Universitas Negeri Gorontalo, Bone Bolango 96119, Indonesia
Nurlaila Zaid Program Studi Matematika, Universitas Negeri Gorontalo, Bone Bolango 96119, Indonesia

DOI:

https://doi.org/10.55657/rmns.v1i2.63

Keywords:

Predator-Prey Model, Holling II-Type , Age Structure, Anti-Predator Behaviour

Abstract

This article discusses the Predator-prey Holling type II model involving age structure and anti-predator behaviour. The age structure is given to the predator population, which is divided into two, namely juvenile predators and adult predators, while in the prey population, there is anti-predator behaviour, namely the tendency to defend against predator attacks. The model analysis includes the determination of a fixed point, analysis of the stability of the fixed point and numerical simulation. Three fixed points were obtained, namely the fixed point of population extinction (), the fixed point of predator extinction and the fixed point of population existence. Stability analysis shows that is always a saddle while and are conditionally stable. Furthermore, it is shown that the two conditions are both stable nodes. At the end, a simulation shows that the population dynamics that occur are highly dependent on the initial conditions of the population and the value of the anti-predator behaviour parameter of the prey population.

Downloads

Download data is not yet available.

References

J. D. Murray, Mathematical Biology: An Introduction, 3rd Edition. New York(US): Springer-Verlaag, 2002.

J. W. Cain and A. M. Reynold, Ordinary and Partial Differential Equation: An Introduction to Dynamical System. Virginia(US): Center For Teaching Excellence, 2010.

G. T. Skalski and J. F. Gilliam, “Functional Respons with Predator Interference: Viable Alternatives to the Holling Type II Model”, Ecology, vol. 82, pp. 3083–3092, 2001.

M. Diska, Analisis Kestabilan Model Mangsa-Pemangsa Dengan Struktur Usia Pemangsa dan Fungsi Respon Monod-Haldane, [Skripsi]. Bogor(ID): Institut Pertanian Bogor, 2018.

H. S. Panigoro, R. Resmawan, A. T. R. Sidik, N. Walangadi, A. Ismail, and C. Husuna, “A Fractional-Order Predator-rey Model with Age Structure on Predator and Nonlinear Harvesting on Prey,” Jambura J. Math., vol. 4, no. 2, pp. 355–366, Jul. 2022, doi: 10.34312/jjom.v4i2.15220.

S. H. Arsyad, R. Resmawan, and N. Achmad, “Analisis Model Predator-Prey Leslie-Gower dengan Pemberian Racun Pada Predator,” J. Ris. dan Apl. Mat., vol. 4, no. 1, pp. 1–16, Apr. 2020, doi: 10.26740/jram.v4n1.p1-16.

H. S. Panigoro, E. Rahmi, N. Achmad, S. L. Mahmud, R. Resmawan, and A. R. Nuha, “A discrete-time fractional-order Rosenzweig-Macarthur predator-prey model involving prey refuge,” Commun. Math. Biol. Neurosci., vol. 2021, no. 1925, 2021, doi: 10.28919/cmbn/6586.

N. Hasan, Resmawan. R and E. Rahmi, “Analisis Kestabilan Model Eko-Epidemiologi dengan Pemanenan Konstan pada Predator”, JMSK, vol. 16, no. 2, pp. 121-142, 2020.

S. Maisaroh, Resmawan, R and E. Rahmi, “Analisis Kestabilan Model Predator-Prey dengan Infeksi Penyakit pada Prey dan Pemanenan Proporsional pada Predator”, JJBM, vol. 1, no. 1, pp. 8-15, 2020.

M. B. Gaib and W. A. Ja’a, “Analisis Kestabilan Model Interaksi Predator-Prey Dengan Fungsi Respon Monod-Haldane Dan Perilaku Anti Pemangsa,” Euler J. Ilm. Mat. Sains dan Teknol., vol. 8, no. 2, pp. 51–59, Dec. 2020, doi: 10.34312/euler.v8i2.10407.

S. G. Mortoja, P. Panja, and S. K. Mondal, “Dynamics of a Predator-Prey Model with Stage-Structure on Both Species and Anti-Predator Behavior”, Informatics in Medicine Unlocked, vol. 10, pp. 50–57, 2018.

I. Djakaria, M. B. Gaib, and R. Resmawan, “Analysis of The Rosenzweig-MacArthur Predator-Prey Model with Anti-Predator Behavior,” CAUCHY, vol. 6, no. 4, pp. 260–269, May 2021, doi: 10.18860/ca.v6i4.11472.