Analisis Bifurkasi Hopf Pada Sistem Keuangan Dengan Kontrol Input

Saputri, Anggita Dwi (2018) Analisis Bifurkasi Hopf Pada Sistem Keuangan Dengan Kontrol Input. Undergraduate thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Sistem Keuangan mempunyai peran penting dalam ekonomi dimana stabilitas sistem keuangan mempengaruhi stabilitas ekonomi. Ketidakstabilan sistem keuangan dapat mengakibatkan timbulnya masalah yang sangat berdampak pada kegiatan ekonomi, seperti krisis keuangan. Penelitian ini menganalisa perilaku dinamis model matematika sistem keuangan. Oleh karena itu, diperlukan adanya kajian terhadap dinamika sistem keuangan dengan menggunakan model matematika untuk mengetahui sistem keuangan yang berkaitan dengan kestabilan sistem. Analisis dinamika model matematika sistem keuangan pada penelitian ini meliputi mencari titik tetap, menentukan kestabilitan titik tetap menggunakan kriteria Routh-Hurwitz, dan analisis bifurkasi Hopf. Bifurkasi Hopf terjadi pada titik tetap E_0. Eksistensi bifurkasi Hopf bergantung pada biaya per investasi di pasar komersial sebagai parameter bifurkasi. Hasil analisis menunjukkan adanya bifurkasi Hopf yang mengelilingi titik tetap positif. Untuk mendukung hasil analisis dilakukan simulasi numerik dengan menggunakan Runge-Kutta orde empat. ============ The financial system has an important role in the economy where the stability of the financial system affect economic stability. The instability of the financial system can lead to the very problem have an impact on economic activities, such as the financial crisis. Therefor, it is necessary to study the dynamics of financial system using mathematical models regard to system stability. This research analyzes the behavior of dynamic mathematical model of the financial system. Dynamics analysis of the mathematical model of the financial system include seeking a fixed point, to determine the stability of a fixed point using the Routh-Hurwitz criterion, the Hopf bifurcation and analysis. Hopf bifurcation occurs at the fixed oint E_0. The result of the analysis shows that there is a Hopf bifurcation that surrounds the positive fixed point. The existence of Hopf bifurcation depending on the cost of investing in the commercial markets as the bifurcation parameter. To support the results of the analysis of the numeric simulation by using fourth order of Runge-Kutta numerical method.

Item Type: Thesis (Undergraduate)
Uncontrolled Keywords: Financial system models; Stability; Hopf Bifurcation; Runge-Kutta Method
Subjects: H Social Sciences > HG Finance > HG4012 Mathematical models
Q Science > QA Mathematics
Divisions: Faculty of Mathematics, Computation, and Data Science > Mathematics > (S1) Undergraduate Theses
Depositing User: Anggita Dwi Saputri
Date Deposited: 20 Jul 2018 03:00
Last Modified: 20 Jul 2018 03:00
URI: http://repository.its.ac.id/id/eprint/52208

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