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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Main Authors: Anjali Jha, Arvind Kumar Misra
Format: Article
Language:English
Published: Vilnius University Press 2025-03-01
Series:Nonlinear Analysis
Subjects:
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
description 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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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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AT arvindkumarmisra mitigatingatmosphericcarbondioxidethroughdeploymentofrenewableenergyamathematicalmodel