Analysis of The Rosenzweig-MacArthur Predator-Prey Model with Anti-Predator Behavior

Djakaria, Ismail; Gaib, Muhammad Bachtiar; Resmawan, Resmawan

doi:10.18860/ca.v6i4.11472

Cited by 2 publications

(1 citation statement)

References 12 publications

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“…Pada penelitian ini dilakukan konstruksi model yang melibatkan interaksi predator-prey yang mengacu pada model yang telah dilakukan sebelumnya pada [10] dengan melakukan mofikasi menggunakan fungsi respon Holling Tipe II. Modifikasi lain dilakukan dengan mempertimbangkan adanya struktur usia pada populasi predator yang merujuk pada [11] serta mempertimbangkan adanya perilaku anti-predator pada populasi prey yang mengacu pada [12]. Kajian terhadap model yang telah dikonstruksi dilakukan dengan menentukan titik tetap dan analisis stabilitasnya, serta pada bagian akhir diberikan simulasi numerik untuk menunjukkan dinamika populasi yang terjadi dari model tersebut.…”

Section: Pendahuluanunclassified

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

Idrus

Gani

Zaid

2022

Res. Math. Nat. Sci.

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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.

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Section: Pendahuluanunclassified

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

Idrus

Gani

Zaid

2022

Res. Math. Nat. Sci.

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Interpretation and Dynamics of the Lotka–Volterra Model in the Description of a Three-Level Laser

et al. 2021

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In this work, the Lotka–Volterra equations where applied to laser physics to describe population inversion and the number of emitted photons. Given that predation and stimulated emissions are analogous processes, two rate equations where obtained by finding suitable parameter transformations for a three-level laser. This resulted in a set of differential equations which are isomorphic to several laser models under accurate parameter identification. Furthermore, the steady state provided two critical points: one where light amplification stops and another where continuous-wave operation is achieved. Lyapunov’s first method of stability yielded the conditions for the convergence to the continuous-wave point, whereas a Lyapunov potential provided its stability regions. Finally, the Q-Switching technique was modeled by introducing a periodic variation of the quality Q of the cavity. This resulted in the transformation of the asymptotically stable fixed point into a limit cycle in the phase space.

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Analysis of The Rosenzweig-MacArthur Predator-Prey Model with Anti-Predator Behavior

Cited by 2 publications

References 12 publications

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

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

Interpretation and Dynamics of the Lotka–Volterra Model in the Description of a Three-Level Laser

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