ANALISIS KESTABILAN MODEL MANGSA-PEMANGSADENGAN FUNGSI RESPON HOLLING TIPE III DANSTRUKTUR UMUR PADA PEMANGSA

HANI PRATIWI, . (2021) ANALISIS KESTABILAN MODEL MANGSA-PEMANGSADENGAN FUNGSI RESPON HOLLING TIPE III DANSTRUKTUR UMUR PADA PEMANGSA. Sarjana thesis, UNIVERSITAS NEGERI JAKARTA.

	Text COVER.pdf Download (2MB)
	Text BAB I.pdf Download (255kB)
	Text BAB II.pdf Restricted to Registered users only Download (414kB) | Request a copy
	Text BAB III.pdf Restricted to Registered users only Download (259kB) | Request a copy
	Text BAB IV.pdf Restricted to Registered users only Download (738kB) | Request a copy
	Text BAB V.pdf Restricted to Registered users only Download (280kB) | Request a copy
	Text DAFTAR PUSTAKA.pdf Download (232kB)
	Text LAMPIRAN.pdf Restricted to Registered users only Download (3MB) | Request a copy

Abstract

Persaingan untuk memperoleh makanan pada peristiwa makan dan dimakan merupakan salah satu kejadian alam yang menjadi topik pembahasan dalam model matematika, yaitu pada model mangsa pemangsa. Dalam tulisan ini dipelajari model mangsa-pemangsa dengan fungsi respon Holling tipe III yang melibatkan satu mangsa dan satu pemangsa dengan struktur umur pada pemangsa, sehingga pemangsa akan dibagi menjadi dua kelompok yaitu pemangsa muda dan pemangsa dewasa. Analisis dilakukan dengan mencari titik tetap dan memeriksa kestabilannya. Titik tetap beserta kestabilannya dianalisis dengan metode linearisasi matriks Jacobi dan analisis kestabilan ditentukan berdasarkan nilai eigen dari persamaan karakteristik sesuai kriteria Routh-Hurwitz. Secara analitik, diperoleh tiga titik tetap yang bemakna, titik tetap T1 selalu bersifat pelana, sedangkan titik tetap T2 dan T3 dapat bersifat pelana dan stabil tergantung pada besarnya nilai koefisien konversi pemangsa. Koefisien konversi pemangsa menyatakan tingkat interaksi mangsa dan pemangsa dewasa yang mengakibatkan penambahan pemangsa remaja. Dari hasil simulasi numerik dengan nilai parameter r = 0.01342, K = 1000, α = 0.0001787, β = 0.0003, γ = 0.09, δ1 = δ2 = 0.0556, ρ = 0.15 dan nilai awal x(0) = 40, y(0) = 25, z(0) = 10 menunjukan bahwa kestabilan titik tetap T1 selalu bersifat pelana, kestabilan titik tetap T2 bersifat stabil jika ρ < 0.1515 dan bersifat pelana jika ρ > 0.1515, dan kestabilan titik tetap T3 bersifat stabil jika dan hanya jika a1 > 0, a3 > 0, dan a1a2 − a3 > 0. Kata kunci : model mangsa-pemangsa, Holling tipe III, struktur umur, titik tetap, Routh-Hurwitz. ----------------------------------------------- Competition to obtain food in eat and eaten is one of nature occurence which becoming central topic of matematical modeling, called predator-prey model. In this paper studied predator-prey model with Holling type III function respon which involves one prey and one predator with age structure of predator, so that predator will be divided into two groups, young predator and adult predator. Analysis is performed by finding a fixed point and checking its stability. Fixed points and their stability were analyzed using the Jacobi matrix linearization method and the stability analysis was determined based on the eigenvalues of the characteristic equations according to the Routh-Hurwitz criteria. Analytically, there are three meaningful fixed points, the fixed point T1 is always saddle, while the fixed point T2 and T3 can be saddle and stable depending on the value of the predatory conversion coefficient. The predator conversion coefficient states the level of interaction between prey and adult predators which results in the addition of juvenile predators. From the numerical simulation results with the parameter value r = 0.01342, K = 1000, α = 0.0001787, β = 0.0003, γ = 0.09, δ1 = δ2 = 0.0556, ρ = 0.15 and the initial value x(0) = 40, y(0) = 25, z(0) = 10 indicates that the stability of the fixed point T1 is always saddle, fixed point stability T2 is stable if rho < 0.1515 and saddle if rho > 0.1515, and the fixed point stability T3 is stable if and only if a1 > 0, a3 > 0, and a1a2 − a3 > 0. Keywords : predator-prey model, Holling type III, age structure, fixed point, Routh-Hurwitz

Item Type:	Thesis (Sarjana)
Additional Information:	1). Ibnu Hadi, M.Si. ; 2). Siti Rohmah Rohiman, S.Pd., M.Si.
Subjects:	Sains > Matematika
Divisions:	FMIPA > S1 Matematika
Depositing User:	Users 9623 not found.
Date Deposited:	01 Mar 2021 03:30
Last Modified:	01 Mar 2021 03:30
URI:	http://repository.unj.ac.id/id/eprint/13737

Actions (login required)

View Item