Maretta, Amira Sarah (2019) Analisis Kestabilan dan Bifurkasi Pada Sistem Keuangan dengan Waktu Tunda. 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. Ketidakteraturan sistem keuangan akan mengakibatkan masalah pada kegiatan ekonomi lainnya. Pada penelitian ini dilakukan analisa perilaku disekitar titik kritis bifurkasi Hopf pada sistem keuangan dengan waktu tunda. Pada sistem keuangan tanpa waktu tunda, dipilih total tabungan di bank sebagai parameter bifurkasi. Total tabungan di bank harus dipertahankan pada tingkat yang tepat agar perkembangan ekonomi lebih baik. Berdasarkan kriteria Routh-Hurwitz, sistem keuangan bersifat stabil ketika nilai total tabungan kurang dari 1 (a<1), bersifat tidak stabil ketika total tabungan di bank lebih dari 1 (a>1), dan sistem terjadi bifrukasi Hopf ketika total tabungan sama dengan 1 (a=1). Selanjutnya, ditambahkan waktu tunda pada tingkat suku bunga dan dipilih waktu tunda sebagai parameter bifurkasi. Hasil penelitian ditemukan bahwa waktu tunda memengaruhi sifat kestabilan sistem keuangan yang mula-mula tidak stabil menjadi stabil ketika nilai waktu tunda τ∈[0,τ_n) dan terjadi bifukasi Hopf dengan nilai waktu tunda τ=τ_n, dimana τ_n=1.993214814 adalah nilai waktu tunda kritis. Analisa tersebut telah direpresentasikan dalam simulasi numerik Runge-Kutta.============================================================================================================The financial system has an important role in the economy, where financial system stability affects economic stability. Financial system irregularities will cause problems in other economic activities. In this study a behavioral analysis was carried out around the critical point of the Hopf bifurcation in the financial system with a delay. In the financial system without time delay, the total savings in the bank are chosen as bifurcation parameters. Total savings in banks must be maintained at the right level so that economic development is better. Based on the Routh-Hurwitz criteria, the financial system is stable when the total value of savings is less than 1 or (a <1), is unstable when the total savings in the bank are more than 1 or (a> 1), and the system occurs bifurcation Hopf if the total savings equals to 1 or (a = 1). Next, the delay time is added to the interest rate and the delay time is chosen as a bifurcation parameter. The results of the study found that the delay time affected the stability of the financial system which was initially unstable when the delay time value τ∈ [0,τ_n ) and Hopf bifukasi occurred with a time delay value τ= τ_n, where τ_n = 1.993214814 is the delay time value critical. The analysis has been represented in the Runge-Kutta numerical simulation.
| Item Type: | Thesis (Undergraduate) |
|---|---|
| Uncontrolled Keywords: | Financial System, Stability, Hopf Bifurcation, Runge-Kutta Method, Delay Time |
| Subjects: | Q Science > QA Mathematics > QA402 System analysis. |
| Divisions: | Faculty of Mathematics and Science > Mathematics > 44201-(S1) Undergraduate Thesis |
| Depositing User: | Amira Sarah Maretta |
| Date Deposited: | 13 Jun 2024 01:45 |
| Last Modified: | 13 Jun 2024 01:45 |
| URI: | http://repository.its.ac.id/id/eprint/67127 |
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