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Dynamic Behavior of Caputo Fractional-Order Model of Forest Biomass, Human Population, and Atmospheric Carbon Dioxide

Communication in Biomathematical Sciences · Vol. 9 No. 1 (2026) · hlm. 15–28

DOI
10.5614/cbms.2026.9.1.2
ISSN
2549-2896
Terbit
2026-05-11
Penerbit
The Indonesian Bio-Mathematical Society
Bahasa
eng
Lisensi
creativecommons.org/licenses/by-nd/4.0

Abstrak

This study aims to analyze the dynamical model of CO2 concentration, human population, and forest biomass. Human activities and land-use changes in forested areas play an important role as the primary contributors to the increase in CO2 emissions, which drive global warming. The inclusion of fractionalorder derivatives is considered to examine the long-term memory effects on the interactions within the CO2 concentration model. Theoretical results such as the existence, uniqueness, positivity, and boundedness of solutions, the local and global stability behavior of equilibrium points, and the existence of a Hopf bifurcation are explored. Furthermore, key parameters, including the deforestation rate and memory order, are investigated to determine their influence on the solution behavior of the CO2 concentration model. A fractionalorder numerical scheme is employed to illustrate various scenarios, validating the theoretical findings. The results show that fractional-order changes affect the dynamic behavior of the model. In addition, increased deforestation rates can increase CO2 concentrations and reduce human population in the long term.

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  • University of Brawijaya
  • State University of Semarang
  • State University of Gorontalo
  • University of Technology Malaysia
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Rekan penulisOrganisasiArtikel bersama
Hasan S. PanigoroState University of Gorontalo7
Trisilowati TrisilowatiUniversity of Brawijaya5
Nuning NurainiAfiliasi tidak diketahui4
Raqqasyi Rahmatullah MusafirUniversity of Brawijaya4
Anggraini MulwindaState University of Semarang3
Resmawan ResmawanState University of Gorontalo3
Agus SuryantoUniversity of Brawijaya2
Mudji SantosaAfiliasi tidak diketahui2
Moch. Dawam MaghfoerAfiliasi tidak diketahui2
Muhammad HarlanuAfiliasi tidak diketahui2
Wuryansari Muharini KusumawinahyuUniversity of Brawijaya2
Hari WibawantoState University of Semarang1
Dania Ayu WulandariState University of Semarang1
Agus MurnomoState University of Semarang1
Bambang SatrioState University of Semarang1
Khoirudin FathoniState University of Semarang1
Suci AstutikUniversity of Brawijaya1
Darmanto DarmantoUniversity of Brawijaya1
Nurjannah NurjannahUniversity of Brawijaya1
Diego IrsandyUniversity of Brawijaya1
Muhammad Hisyam LeeUniversity of Technology Malaysia1
Rismania Hartanti Putri Yulianing DamayantiUniversity of Brawijaya1
Marsudi MarsudiUniversity of Brawijaya1
Syaiful AnamUniversity of Brawijaya1
Ach. KhozaimiUniversity of Brawijaya1
Nur ShofianahUniversity of Brawijaya1
Onik Febria DamayantiUniversity of Brawijaya1
Noor HudallahAfiliasi tidak diketahui1
Diah ErvianiAfiliasi tidak diketahui1
Riris YuniaratriAfiliasi tidak diketahui1
Ulfah Mediaty AriefState University of Semarang1
Bayu Ari PranataAfiliasi tidak diketahui1
Triska Widya IndriyaniAfiliasi tidak diketahui1
Muhamad JaeniAfiliasi tidak diketahui1
Ahmad Ubaedi FathudinAfiliasi tidak diketahui1
Ali BurhanAfiliasi tidak diketahui1

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Sumber metadata: OAI-PMH (metadata jurnal) http://journals.itb.ac.id/index.php/cbms/oai, pertama di-harvest 8 Nov 2026, terakhir terlihat 8 Nov 2026.
Metadata asli (oai_dc) 
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	<dc:title xml:lang="en-US">Dynamic Behavior of Caputo Fractional-Order Model of Forest Biomass, Human Population, and Atmospheric Carbon Dioxide</dc:title>
	<dc:creator>Huda, Moh. Nurul</dc:creator>
	<dc:creator>Suryanto, Agus</dc:creator>
	<dc:creator>Darti, Isnani</dc:creator>
	<dc:creator>Fakhruddin, Muhammad</dc:creator>
	<dc:subject xml:lang="en-US">carbon dioxide</dc:subject>
	<dc:subject xml:lang="en-US">deforestation</dc:subject>
	<dc:subject xml:lang="en-US">forest biomass</dc:subject>
	<dc:subject xml:lang="en-US">global stability</dc:subject>
	<dc:subject xml:lang="en-US">Hopf bifurcation</dc:subject>
	<dc:subject xml:lang="en-US">26A33</dc:subject>
	<dc:subject xml:lang="en-US">34D23</dc:subject>
	<dc:subject xml:lang="en-US">34C23</dc:subject>
	<dc:subject xml:lang="en-US">92B05</dc:subject>
	<dc:subject xml:lang="en-US">92D40</dc:subject>
	<dc:description xml:lang="en-US">This study aims to analyze the dynamical model of CO2 concentration, human population, and forest biomass. Human activities and land-use changes in forested areas play an important role as the primary contributors to the increase in CO2 emissions, which drive global warming. The inclusion of fractionalorder derivatives is considered to examine the long-term memory effects on the interactions within the CO2 concentration model. Theoretical results such as the existence, uniqueness, positivity, and boundedness of solutions, the local and global stability behavior of equilibrium points, and the existence of a Hopf bifurcation are explored. Furthermore, key parameters, including the deforestation rate and memory order, are investigated to determine their influence on the solution behavior of the CO2 concentration model. A fractionalorder numerical scheme is employed to illustrate various scenarios, validating the theoretical findings. The results show that fractional-order changes affect the dynamic behavior of the model. In addition, increased deforestation rates can increase CO2 concentrations and reduce human population in the long term.</dc:description>
	<dc:publisher xml:lang="en-US">The Indonesian Bio-Mathematical Society</dc:publisher>
	<dc:date>2026-05-11</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:type xml:lang="en-US">Peer-reviewed Article</dc:type>
	<dc:format>application/octet-stream</dc:format>
	<dc:identifier>https://journals.itb.ac.id/index.php/cbms/article/view/27312</dc:identifier>
	<dc:identifier>10.5614/cbms.2026.9.1.2</dc:identifier>
	<dc:source xml:lang="en-US">Communication in Biomathematical Sciences; Vol. 9 No. 1 (2026); 15-28</dc:source>
	<dc:source>2549-2896</dc:source>
	<dc:source>10.5614/cbms.2026.9.1</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://journals.itb.ac.id/index.php/cbms/article/view/27312/7372</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2026 Communication in Biomathematical Sciences</dc:rights>
	<dc:rights xml:lang="en-US">https://creativecommons.org/licenses/by-nd/4.0</dc:rights>
</oai_dc:dc>