{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T03:13:15Z","timestamp":1792033995100,"version":"4.4.0"},"reference-count":40,"publisher":"AIP Publishing","issue":"10","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12471465"],"award-info":[{"award-number":["12471465"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Shanghai","award":["23ZR1445100"],"award-info":[{"award-number":["23ZR1445100"]}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,10,1]]},"abstract":"<jats:p>Mitigating carbon dioxide (CO2) emissions associated with energy generation is crucial for addressing the climate crisis. To better understand the dynamic relationship between CO2 concentration, human population, and energy consumption in a stochastic environment, we propose and investigate a stochastic carbon emissions model and further consider its near-optimal control (NOC) problem. We first focus on the natural evolution scenario without intervention measures to analyze the dynamic behavior of the carbon emissions system under environmental fluctuations. The results suggest that when environment noise is sufficiently large (such that \u03d5&amp;lt;0), it will lead the population to collapse, thereby reducing energy consumption to zero, and eventually returning CO2 concentration to pre-industrial level. This is an unsustainable scenario ecologically for the model. When environment noise is not too large (such that \u03d6&amp;gt;0), there exists a unique ergodic stationary distribution. To effectively reduce the CO2 concentration while ensuring a reasonable population size, we then develop a NOC system that incorporates two intervention strategies. Using the Pontryagin stochastic maximum principle, we establish necessary and sufficient conditions for the existence of the near-optimality. Theoretical and numerical results demonstrate that effective CO2 mitigation strategies must consider both ecological sustainability and economic feasibility. From the perspective of policymakers, this study emphasizes the importance of dynamically adjusting emission reduction strategies across different development stages. Such adaptive decision-making can effectively alleviate atmospheric CO2 concentration while ensuring economic and ecological sustainability.<\/jats:p>","DOI":"10.1063\/5.0292883","type":"journal-article","created":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T12:55:49Z","timestamp":1759323349000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Dynamical analysis and near-optimal control strategy of a stochastic carbon emissions model"],"prefix":"10.1063","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-4226-9753","authenticated-orcid":false,"given":"Xinxin","family":"Wang","sequence":"first","affiliation":[{"name":"College of Science, University of Shanghai for Science and Technology 1 , Shanghai 200093,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0510-1428","authenticated-orcid":false,"given":"Tonghua","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Swinburne University of Technology 2 , Hawthorn, Victoria 3122,","place":["Australia"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0502-3653","authenticated-orcid":false,"given":"Sanling","family":"Yuan","sequence":"additional","affiliation":[{"name":"College of Science, University of Shanghai for Science and Technology 1 , Shanghai 200093,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2025,10,1]]},"reference":[{"key":"2025100108554328400_c1","author":"International Energy Agency"},{"key":"2025100108554328400_c2","doi-asserted-by":"publisher","first-page":"981","DOI":"10.1002\/ird.2597","article-title":"Impacts of population growth and climate change on food production and irrigation and drainage needs: A world-wide view","volume":"70","year":"2021","journal-title":"Irrig. Drain."},{"key":"2025100108554328400_c3","author":"International Energy Agency"},{"key":"2025100108554328400_c4","doi-asserted-by":"publisher","first-page":"100965","DOI":"10.1016\/j.pecs.2021.100965","article-title":"Carbon dioxide emissions, capture, storage and utilization: Review of materials, processes and technologies","volume":"89","year":"2022","journal-title":"Prog. Energy Combust. Sci."},{"key":"2025100108554328400_c5","doi-asserted-by":"publisher","first-page":"8595","DOI":"10.1016\/j.amc.2013.02.058","article-title":"A mathematical model to study the dynamics of carbon dioxide gas in the atmosphere","volume":"219","year":"2013","journal-title":"Appl. Math. Comput."},{"key":"2025100108554328400_c6","doi-asserted-by":"publisher","first-page":"1435","DOI":"10.15666\/aeer\/2002_14351455","article-title":"Modelling energy consumption and carbon dioxide emissions of fossil fuels and nuclear energy using Lotka-Volterra equations","volume":"20","year":"2022","journal-title":"Appl. Ecol. Environ. Res."},{"key":"2025100108554328400_c7","doi-asserted-by":"publisher","first-page":"110279","DOI":"10.1016\/j.ecolmodel.2023.110279","article-title":"Dynamics of a coupled socio-environmental model: An application to global CO2 emissions","volume":"478","year":"2023","journal-title":"Ecol. Model."},{"key":"2025100108554328400_c8","doi-asserted-by":"publisher","first-page":"021101","DOI":"10.1063\/5.0135266","article-title":"Predicting climatic tipping points","volume":"33","year":"2023","journal-title":"Chaos"},{"key":"2025100108554328400_c9","doi-asserted-by":"publisher","first-page":"13919","DOI":"10.1007\/s10668-021-01245-y","article-title":"Mathematical modeling and optimal control of carbon dioxide emissions from energy sector","volume":"23","year":"2021","journal-title":"Environ. Develop. Sustain."},{"key":"2025100108554328400_c10","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1038\/s41560-020-0558-0","article-title":"Quantifying the impacts of climate change and extreme climate events on energy systems","volume":"5","year":"2020","journal-title":"Nat. Energy"},{"key":"2025100108554328400_c11","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1038\/s41560-020-0562-4","article-title":"Event-based models to understand the scale of the impact of extremes","volume":"5","year":"2020","journal-title":"Nat. Energy"},{"key":"2025100108554328400_c12","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1038\/s41560-020-0555-3","article-title":"Energy modellers should explore extremes more systematically in scenarios","volume":"5","year":"2020","journal-title":"Nat. Energy"},{"key":"2025100108554328400_c13","doi-asserted-by":"publisher","first-page":"103642","DOI":"10.1016\/j.euroecorev.2020.103642","article-title":"Optimal carbon abatement in a stochastic equilibrium model with climate change","volume":"132","year":"2021","journal-title":"Eur. Econ. Rev."},{"key":"2025100108554328400_c14","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s43546-023-00512-6","article-title":"A climate\u2013economy model in a stochastic differential equilibrium with fractional Brownian motions and Poisson jumps","volume":"3","year":"2023","journal-title":"SN Business Econ."},{"key":"2025100108554328400_c15","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1038\/nclimate2249","article-title":"Optimal CO2 mitigation under damage risk valuation","volume":"4","year":"2014","journal-title":"Nature Climate Change"},{"key":"2025100108554328400_c16","doi-asserted-by":"publisher","first-page":"8177","DOI":"10.1016\/j.jfranklin.2018.09.013","article-title":"Stationary distribution and extinction of a stochastic predator\u2013prey model with herd behavior","volume":"355","year":"2018","journal-title":"J. Franklin Inst."},{"key":"2025100108554328400_c17","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1007\/s00285-021-01589-z","article-title":"Dynamics of task allocation in social insect colonies: Scaling effects of colony size versus work activities","volume":"82","year":"2021","journal-title":"J. Math. Biol."},{"key":"2025100108554328400_c18","doi-asserted-by":"publisher","first-page":"107157","DOI":"10.1016\/j.cnsns.2023.107157","article-title":"Stationary distribution, density function and extinction of stochastic vegetation-water systems","volume":"120","year":"2023","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"2025100108554328400_c19","doi-asserted-by":"publisher","first-page":"123116","DOI":"10.1063\/5.0168714","article-title":"Modeling the role of renewable energy to mitigate the atmospheric level of carbon dioxide along with sustainable development","volume":"33","year":"2023","journal-title":"Chaos"},{"key":"2025100108554328400_c20","doi-asserted-by":"publisher","first-page":"212726","DOI":"10.1016\/j.geoen.2024.212726","article-title":"Recent advances in CCUS: A critical review on technologies, regulatory aspects and economics","volume":"238","year":"2024","journal-title":"Geoenergy Sci. Eng."},{"key":"2025100108554328400_c21","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1109\/TAC.1986.1104206","article-title":"Optimal control of production rate in a failure prone manufacturing system","volume":"31","year":"1986","journal-title":"IEEE Trans. Autom. Control"},{"key":"2025100108554328400_c22","doi-asserted-by":"publisher","first-page":"13313","DOI":"10.1002\/mma.10192","article-title":"The dynamics and near-optimal controls of a dengue model with threshold policy","volume":"47","year":"2024","journal-title":"Math. Methods Appl. Sci."},{"key":"2025100108554328400_c23","doi-asserted-by":"publisher","first-page":"678","DOI":"10.1111\/sapm.12517","article-title":"Near-optimal control of a stochastic model for mountain pine beetles with pesticide application","volume":"149","year":"2022","journal-title":"Stud. Appl. Math."},{"key":"2025100108554328400_c24","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1016\/j.apm.2019.10.013","article-title":"Sufficient and necessary conditions for stochastic near-optimal controls: A stochastic chemostat model with non-zero cost inhibiting","volume":"78","year":"2020","journal-title":"Appl. Math. Model."},{"key":"2025100108554328400_c25","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1007\/s40435-015-0179-9","article-title":"Sufficient condition for near-optimal control of general controlled linear forward\u2013backward stochastic differential equations","volume":"5","year":"2017","journal-title":"Int. J. Dyn. Control"},{"key":"2025100108554328400_c26","doi-asserted-by":"publisher","first-page":"100752","DOI":"10.1016\/j.ejcon.2022.100752","article-title":"Near-optimal control of a stochastic partial differential equation SEIR epidemic model under economic constraints","volume":"69","year":"2023","journal-title":"Eur. J. Control"},{"key":"2025100108554328400_c27","doi-asserted-by":"publisher","first-page":"101097","DOI":"10.1016\/j.ejcon.2024.101097","article-title":"Investigation of sliding mode dynamics and near-optimal controls for a reaction\u2013diffusion population model in a polluted environment","volume":"79","year":"2024","journal-title":"Eur. J. Control"},{"key":"2025100108554328400_c28","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1007\/s10492-014-0064-4","article-title":"On near-optimal necessary and sufficient conditions for forward-backward stochastic systems with jumps, with applications to finance","volume":"59","year":"2014","journal-title":"Appl. Math."},{"key":"2025100108554328400_c29","volume-title":"Stochastic Differential Equations and Applications","year":"2007"},{"key":"2025100108554328400_c30","volume-title":"Stochastic Controls: Hamiltonian Systems and HJB Equations","year":"1999"},{"key":"2025100108554328400_c31","volume-title":"Optimization and Nonsmooth Analysis","year":"1990"},{"key":"2025100108554328400_c32","author":"NOAA Earth System Research Laboratory"},{"key":"2025100108554328400_c33"},{"key":"2025100108554328400_c34"},{"key":"2025100108554328400_c35","volume-title":"Climate Change 2001: The Scientific Basis","author":"Intergovernmental Panel on Climate Change (IPCC)","year":"2001"},{"key":"2025100108554328400_c36"},{"key":"2025100108554328400_c37","doi-asserted-by":"publisher","first-page":"4467","DOI":"10.1038\/s41467-021-24487-w","article-title":"The mortality cost of carbon","volume":"12","year":"2021","journal-title":"Nat. Commun."},{"key":"2025100108554328400_c38","doi-asserted-by":"publisher","first-page":"66","DOI":"10.3390\/environments10040066","article-title":"The rising threat of atmospheric CO2: A review on the causes, impacts, and mitigation strategies","volume":"10","year":"2023","journal-title":"Environments"},{"key":"2025100108554328400_c39","doi-asserted-by":"publisher","first-page":"2069","DOI":"10.1007\/s10311-020-01059-w","article-title":"Strategies for mitigation of climate change: A review","volume":"18","year":"2020","journal-title":"Environ. Chem. Lett."},{"key":"2025100108554328400_c40","doi-asserted-by":"publisher","first-page":"876","DOI":"10.1137\/10081856X","article-title":"A stochastic differential equation SIS epidemic model","volume":"71","year":"2011","journal-title":"SIAM J. Appl. Math."}],"container-title":["Chaos: An Interdisciplinary Journal of Nonlinear Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0292883\/20724208\/103103_1_5.0292883.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/cha\/article-pdf\/doi\/10.1063\/5.0292883\/20724208\/103103_1_5.0292883.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T12:55:51Z","timestamp":1759323351000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/cha\/article\/35\/10\/103103\/3365576\/Dynamical-analysis-and-near-optimal-control"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,1]]},"references-count":40,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2025,10,1]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0292883","relation":{},"ISSN":["1054-1500","1089-7682"],"issn-type":[{"value":"1054-1500","type":"print"},{"value":"1089-7682","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025,10]]},"published":{"date-parts":[[2025,10,1]]},"article-number":"103103"}}