Analisis Kestabilan Model Interaksi Predator-Prey Dengan Fungsi Respon Monod-Haldane Dan Perilaku Anti Pemangsa

Abstract

This article examines a competing prey-predator model using the Monod-Haldane response function and anti-predator behavior. This article discusses equilibrium point determination, equilibrium point stability analysis, and numerical simulation. Obtained three equilibrium points, namely T1, T2, and T3, where the equilibrium-point is always saddle, the stability of the equilibrium points T2 and T3 will be stable if it meets the predetermined parameter requirements. There are two cases in the equilibrium point where the first case is vertically stable and the second case is spiral stable.

Dynamic Analysis of a Prey Predator Model with Holling-Type III Functional Response and Anti-Predator Behavior

“…The system (1) can exhibit bistability at η = 0.1. In Figure (2) and Figure (3), the system has double stability, namely bistable at 𝐸 1 and 𝐸 2 influenced by differences in initial values. Figure (2) shows the solution from a convergent system to an equilibrium point 𝐸 1 (7.5,0) using initial values 𝑁 1 [17,17] so that the equilibrium point 𝐸 1 is stable.…”

“…In Figure (2) and Figure (3), the system has double stability, namely bistable at 𝐸 1 and 𝐸 2 influenced by differences in initial values. Figure (2) shows the solution from a convergent system to an equilibrium point 𝐸 1 (7.5,0) using initial values 𝑁 1 [17,17] so that the equilibrium point 𝐸 1 is stable. Figure 3 shows the solution from a convergent system to an equilibrium point 𝐸 3 (0.04, 4.66) using initial values 𝑁 2 [1,17] so that the equilibrium point 𝐸 2 is stable.…”

“…The characteristic equation of 𝐽 𝐸 2 is given by: 𝜆 2 + 𝜏𝜆 + 𝜎 = 0, (7) From characteristic equation (7), the eigenvalue of 𝐽 𝐸 2 are given by: 𝜆 1,2 = (𝜏)±√(𝜏) 2…”

“…Animals that eat other animals are called predators, while animals that other animals hunt are called prey [1]. The purpose of interaction between predators and their prey is to control the density of prey populations to maintain their lives [2], [3].…”

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

“…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].…”