Analisis Pengaruh Urbanisasi dan Pertumbuhan Populasi pada Model Swasembada Pangan

Nurhanipah, Rika (2019) Analisis Pengaruh Urbanisasi dan Pertumbuhan Populasi pada Model Swasembada Pangan. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Model swasembada pangan merupakan model yang terdiri tiga variabel keadaan yaitu jumlah penduduk, jumlah urbanisasi, dan jumlah produksi pangan. Dalam penelitian ini dilakukan analisis mengenai kestabilan dan eksistensi bifurkasi Hopf pada sistem swasembada pangan. Analisis mengenai kestabilan dan bifurkasi Hopf digunakan untuk mengetahui faktor apa yang mempengaruhi terjadinya bifurkasi pada sistem. Analisis kestabilan dapat dilakukan dengan menggunakan kriteria Routh – Hurwitz. Dari hasil analisis didapatkan bahwa eksistensi bifurkasi Hopf terjadi pada titik setimbang (X^*,Y^*,P^*). Eksistensi bifurkasi bergantung pada nilai parameter jumlah petani yang lebih dahulu urbanisasi β_2 sebagai parameter bifurkasi Hopf. Hasil yang didapatkan selanjutnya disimulasikan dengan MATLAB. Berdasarkan dari hasil analisis simulasi didapat jika nilai β_2≥41 menyebabkan jumlah urbanisasi bertambah dan jika nilai β_2≤29 menyebabkan jumlah urbanisasi berkurang.
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The food self-sufficiency model is a model that consists of three state variables, they are population, the amount of urbanization, and the amount of food. In this study an analysis of the stability and existence of the Hopf bifurcation was carried out on the food self-sufficiency system. Analysis of stability and Hopf bifurcation is used to determine what factors influence the occurrence of bifurcation in the system. Stability analysis can be done using Routh - Hurwitz criteria. From the results of the analysis it was found that the existence of the Hopf bifurcation occurs at the equilibrium point (X^*,Y^*,P^*). The existence of bifurcation depends on the value of farmers who are urabnized first β_2 as a parameter of Hopf bifurcation. The results obtained are then simulated with MATLAB. Based on the results of the simulation analysis obtained if β_2≥41 causes the amount of urbanization to increase and if β_2≤29 causes the amount of urbanization to decrease.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Bifurkasi Hopf, swasembada pangan, urbanisasi
Subjects:	Q Science > QA Mathematics > QA402 System analysis. S Agriculture > S Agriculture (General)
Divisions:	Faculty of Mathematics and Science > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Nurhanipah Rika
Date Deposited:	06 Aug 2026 04:21
Last Modified:	06 Aug 2026 04:22
URI:	http://repository.its.ac.id/id/eprint/67999

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