https://doi.org/10.1140/epjp/s13360-025-06881-1
Regular Article
Mitigating atmospheric carbon dioxide through ocean-based carbon capture technologies: a delay mathematical model
Department of Mathematics, School of Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, 226025, Lucknow, India
a
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Received:
24
June
2025
Accepted:
18
September
2025
Published online:
1
October
2025
The ocean serves as the largest natural sink for atmospheric carbon dioxide (
), playing a vital role in regulating global climate. Ocean-based carbon removal technologies seek to enhance this natural capacity, while shellfish farming offers a complementary nature-based pathway to sequester carbon dioxide. The success of these strategies, however, depends on effective budget allocation. In this study, we develop a nonlinear mathematical model to examine how budget allocation for ocean-based carbon removal technologies and shellfish farming, along with delays between investment and impact, influences atmospheric dynamics. The model considers that a portion of total budget is allocated for the implementation of ocean-based carbon removal technologies, while the remainder is invested in shellfish farming. The formulated model is qualitatively analyzed to determine the system’s behavior in the long run. Results show that increasing the efficacy of allocated budget in enhancing oceanic uptake and shellfish production can substantially lowers atmospheric levels. However, if the budget growth rate exceeds a critical threshold, the interior equilibrium loses stability through a Hopf-bifurcation, giving rise to limit cycle oscillations. Moreover, it is noticed that the amplitude of these oscillations reduces with increasing the efficacy of budget to enhance oceanic uptake, and above a critical level, these oscillations die out and system gets stabilized to a positive equilibrium state. Furthermore, we find that the stability of the interior equilibrium is highly sensitive to delays between budget allocation and the resulting increase in oceanic 
absorption and shellfish production. Longer delays trigger multiple stability switches, leading to complex dynamic behavior. Numerical simulations are presented to support and validate the theoretical findings, providing insights into the dynamic behavior of the proposed model.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
