Mitigating atmospheric carbon dioxide through deployment of renewable energy: A mathematical model
In recent decades, the widespread reliance on fossil fuels has grown substantially, leading to a rise in atmospheric carbon dioxide (CO2), which poses a major global concern. In this study, we develop and analyze a novel mathematical model to examine the interactions between atmospheric CO2, human...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2025-03-01
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| Series: | Nonlinear Analysis |
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| Online Access: | https://www.journals.vu.lt/nonlinear-analysis/article/view/38975 |
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| author | Anjali Jha Arvind Kumar Misra |
| author_facet | Anjali Jha Arvind Kumar Misra |
| author_sort | Anjali Jha |
| collection | DOAJ |
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In recent decades, the widespread reliance on fossil fuels has grown substantially, leading to a rise in atmospheric carbon dioxide (CO2), which poses a major global concern. In this study, we develop and analyze a novel mathematical model to examine the interactions between atmospheric CO2, human population, and energy demand. The model assumes that human activities and energy production from traditional sources (oil, coal, and gas) contribute to increasing CO2 level, while a shift in energy dependence from traditional to renewable sources (hydro, solar, etc.) occurs as a result of environmental awareness. We derive sufficient conditions for both local and global stability of the system’s interior equilibrium. Numerical simulations demonstrate that when reliance on renewable energy sources is low, the system can exhibit oscillatory dynamics and various bifurcations. However, beyond a critical threshold of renewable energy dependency, the system stabilizes around the interior equilibrium, leading to a reduction in atmospheric CO2. Additionally, an optimal control problem is formulated to reduce atmospheric CO2 level while minimizing the associated implementation costs.
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| format | Article |
| id | doaj-art-164306e0bd7d4d7c96fdece4f4f1d1e3 |
| institution | DOAJ |
| issn | 1392-5113 2335-8963 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj-art-164306e0bd7d4d7c96fdece4f4f1d1e32025-08-20T03:17:18ZengVilnius University PressNonlinear Analysis1392-51132335-89632025-03-013010.15388/namc.2025.30.38975Mitigating atmospheric carbon dioxide through deployment of renewable energy: A mathematical modelAnjali Jha0Arvind Kumar Misra1https://orcid.org/0000-0002-2885-9955Banaras Hindu UniversityBanaras Hindu University In recent decades, the widespread reliance on fossil fuels has grown substantially, leading to a rise in atmospheric carbon dioxide (CO2), which poses a major global concern. In this study, we develop and analyze a novel mathematical model to examine the interactions between atmospheric CO2, human population, and energy demand. The model assumes that human activities and energy production from traditional sources (oil, coal, and gas) contribute to increasing CO2 level, while a shift in energy dependence from traditional to renewable sources (hydro, solar, etc.) occurs as a result of environmental awareness. We derive sufficient conditions for both local and global stability of the system’s interior equilibrium. Numerical simulations demonstrate that when reliance on renewable energy sources is low, the system can exhibit oscillatory dynamics and various bifurcations. However, beyond a critical threshold of renewable energy dependency, the system stabilizes around the interior equilibrium, leading to a reduction in atmospheric CO2. Additionally, an optimal control problem is formulated to reduce atmospheric CO2 level while minimizing the associated implementation costs. https://www.journals.vu.lt/nonlinear-analysis/article/view/38975carbon dioxideenergyLyapunov’s stabilityoptimal control |
| spellingShingle | Anjali Jha Arvind Kumar Misra Mitigating atmospheric carbon dioxide through deployment of renewable energy: A mathematical model Nonlinear Analysis carbon dioxide energy Lyapunov’s stability optimal control |
| title | Mitigating atmospheric carbon dioxide through deployment of renewable energy: A mathematical model |
| title_full | Mitigating atmospheric carbon dioxide through deployment of renewable energy: A mathematical model |
| title_fullStr | Mitigating atmospheric carbon dioxide through deployment of renewable energy: A mathematical model |
| title_full_unstemmed | Mitigating atmospheric carbon dioxide through deployment of renewable energy: A mathematical model |
| title_short | Mitigating atmospheric carbon dioxide through deployment of renewable energy: A mathematical model |
| title_sort | mitigating atmospheric carbon dioxide through deployment of renewable energy a mathematical model |
| topic | carbon dioxide energy Lyapunov’s stability optimal control |
| url | https://www.journals.vu.lt/nonlinear-analysis/article/view/38975 |
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