Analisis sensitivitas dan kestabilan global menggunakan fungsi Lyapunov pada model perilaku kawanan mangsa

Hindanah, Yuli Siti (2022) Analisis sensitivitas dan kestabilan global menggunakan fungsi Lyapunov pada model perilaku kawanan mangsa. Sarjana thesis, UIN Sunan Gunung Djati Bandung.

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Abstract

Skripsi ini membahas model mangsa pemangsa dengan aktifitas kawanan mangsa. Dalam beberapa situasi ekologi, interaksi antara mangsa dan pemangsa terjadi diluar dari kawanan mangsa yang dibentuk oleh populasi mangsa. Mangsa yang membentuk kawanan berfungsi untuk melindungi diri dari serangan pemangsa. Pada model ini terbagi atas dua kompartemen, yaitu x (mangsa) dan y (pemangsa). Analisis yang dilakukan yaitu fungsi respon Holling tipe II tetapi istilah kepadatan mangsa diganti dengan akar kuadrat dari populasi mangsa kemudian analisis sensitivitas untuk mencari parameter yang sensitif serta analisis kestabilan lokal maupun global. Pada analisis kestabilan lokal setiap titik tetap memiliki tiga titik tetap yaitu E_0,E_1,E_(2 )dengan menggunakan matriks Jacobi dan analisis kestabilan global yang setiap titik tetapnya memiliki tiga titik tetap yaitu E_0,E_1,E_(2 )dengan menggunakan kriteria kestabilan Lyapunov atau fungsi Lyapunov. Analisis matematis serta perhitungan numarik disajikan untuk memvalidasi model perilaku kawanan mangsa. Sedangkan untuk mencari titik tetap, analisis eksistensi dan analisis kestabilan lokal serta analisis sensitivitas selain menggunakan teori juga dibantu menggunakan MAPLE. This thesis discusses the prey-predator model with the activity of a herd of prey. In some ecological situations, interactions between prey and predators occur outside of the prey swarm formed by the prey population. Prey that form a herd serves to protect themselves from predator attacks. This model is divided into two compartments, namely x (prey) and y (predator). The analysis carried out is a type II Holling response function but the term prey density is replaced by the square root of the prey population then sensitivity analysis to find sensitive parameters and local and global stability analysis. In local stability analysis, each fixed point has three fixed points, namely E_0,E_1,E_(2 )using the Jacobi matrix and global stability analysis where each fixed point has three fixed points, namely E_0,E_1,E_(2 )using the Lyapunov stability criteria or the Lyapunov function. Mathematical analysis as well as numerical calculations are presented to validate the prey herd behavior model. Meanwhile, to find a fixed point, existence analysis and local stability analysis as well as sensitivity analysis, apart from using theory, are also assisted by using MAPLE.

Item Type: Thesis (Sarjana)
Uncontrolled Keywords: Sistem Mangsa-Pemangsa; Kawanan Mangsa; Titik Tetap; Eksistensi; Matriks Jacobi; Fungsi Lyapunov; Kestabilan Lokal; Kestabilan Global
Subjects: Mathematics
Mathematics > Data Processing and Analysis of Mathematics
Divisions: Fakultas Sains dan Teknologi > Program Studi Matematika
Depositing User: Yuli Siti Hindanah
Date Deposited: 02 Mar 2022 06:56
Last Modified: 02 Mar 2022 06:56
URI: https://digilib.uinsgd.ac.id/id/eprint/49368

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