Analisis kestabilan global menggunakan Lyapunov pada model mangsa pemangsa dengan Stage Structure dan fungsi respon tipe Crowley Martin

Aeni, Dewina Nur (2021) Analisis kestabilan global menggunakan Lyapunov pada model mangsa pemangsa dengan Stage Structure dan fungsi respon tipe Crowley Martin. Sarjana thesis, UIN Sunan Gunung Djati Bandung.

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Abstract

INDONESIA : Tugas akhir ini membahas model mangsa pemangsa dengan fungsi respon tipe Crowley-Martin yang melibatkan tiga subpopulasi, yaitu x (mangsa remaja), y (mangsa dewasa), dan z (pemangsa). Model tersebut akan dianalisis titik kesetimbangannya, dan akan ditentukan jenis kestabilan dari setiap titik kesetimbangan tersebut. Analisis kestabilan lokal dilakukan dengan melihat nilai Eigen dari matriks Jacobi, sementara analisis kestabilan global dilakukan dengan menggunakan fungsi Lyapunov. Analisis sensitivitas dilakukan untuk menyelidiki parameter yang lebih berpengaruh dalam model yang dibangun. Berdasarkan hasil analisis dan interpretasi dapat disimpulkan bahwa titik koeksistensi bersifat stabil asimtotik global jika memenuhi y>1/α ((rx^*)/y^* -μ_2-αy^* ). Selanjutnya dari hasil simulasi diperoleh bahwa, jika laju transisi yaitu r meningkat, maka pertumbuhan populasi mangsa remaja menurun, sedangkan pertumbuhan populasi mangsa dewasa dan pemangsa meningkat. ENGLISH : This thesis discusses a prey-predator model with a Crowley-Martin-type response function involving three subpopulations, namely x (juvenile prey), y (adult prey), and z (predator). The model will be analyzed for its equilibrium points, and the type of stability of each equilibrium point will be determined. The local stability analysis is carried out by looking at the Eigen values of the Jacobi matrix, while global stability analysis is carried out using the Lyapunov function. Sensitivity analysis was carried out to investigate which parameters were more influential in the built model. Based on the results of the analysis and interpretation, it can be concluded that the coexistence point is globally asymptotically stable if it satisfy the equation y>1/α ((rx^*)/y^* -μ_2-αy^* ). Furthermore, the simulation results shown that, if the transition rate i.e. r increases, the juvenile prey population growth decreases, while the adult prey and predator population growth increases.

Item Type: Thesis (Sarjana)
Uncontrolled Keywords: Titik kesetimbangan; kestabilan; fungsi respon tipe Crowley Martin; fungsi lyapunov; sensitivitas.
Subjects: Mathematics
Ecology > Competition Ecological
Ecology > Population Biology
Divisions: Fakultas Sains dan Teknologi > Program Studi Matematika
Depositing User: Dewina Nur Aeni
Date Deposited: 12 Sep 2021 23:20
Last Modified: 13 Sep 2021 00:18
URI: http://digilib.uinsgd.ac.id/id/eprint/43251

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