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All Journal JURNAL DERIVAT: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA
Vivi Ramdhani
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Analisis Kestabilan Model Penipisan Sumber Daya Hutan Dengan Mempertimbangkan Faktor Migrasi Penduduk Vivi Ramdhani
Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika Vol. 12 No. 1 (2025): Jurnal Derivat (April 2025) In Press
Publisher : Pendidikan Matematika Universitas PGRI Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31316/j.derivat.v12i1.7202

Abstract

This article is presented a depletion model of forest resource (B) due to population (N) and population pressure (P), as well as the impact of industrialization (I) by taking into account population migration factors on population rates (N) due to the availability of industry. The method used in this article is through literature study. Based on the analysis model, 4 non-negative fixed points are obtained, namely and  Next, the stability of the four fixed points is explained . The analysis results reveal that the fixed points dan   are types of saddle point fixed points and are unstable. Meanwhile, the stability of the fixed point  is explained using a numerical calculation approach because it is not easy to describe it analytically. In the final part, a numerical simulation was carried out on the balance point and it was found that the stability of forest resources decreased along with the increase in population and population pressure and industrialization. The availability of forest resources has a positive effect on population levels. However, population growth will increase because it is influenced by population migration factors which cause a decline in forest resources. Therefore, it is necessary to control the population rate in order to protect forest resources from extinction. Keywords: Fixed point, Forest resources, Population migration,  Stability.
Analisis Kestabilan Model Penipisan Sumber Daya Hutan Dengan Mempertimbangkan Faktor Migrasi Penduduk Vivi Ramdhani
Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika Vol. 12 No. 1 (2025): Jurnal Derivat (April 2025)
Publisher : Pendidikan Matematika Universitas PGRI Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31316/j.derivat.v12i1.7202

Abstract

This article is presented a depletion model of forest resource (B) due to population (N) and population pressure (P), as well as the impact of industrialization (I) by taking into account population migration factors on population rates (N) due to the availability of industry. The method used in this article is through literature study. Based on the analysis model, 4 non-negative fixed points are obtained, namely and  Next, the stability of the four fixed points is explained . The analysis results reveal that the fixed points dan   are types of saddle point fixed points and are unstable. Meanwhile, the stability of the fixed point  is explained using a numerical calculation approach because it is not easy to describe it analytically. In the final part, a numerical simulation was carried out on the balance point and it was found that the stability of forest resources decreased along with the increase in population and population pressure and industrialization. The availability of forest resources has a positive effect on population levels. However, population growth will increase because it is influenced by population migration factors which cause a decline in forest resources. Therefore, it is necessary to control the population rate in order to protect forest resources from extinction. Keywords: Fixed point, Forest resources, Population migration,  Stability.
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