Dynamical analysis and near-optimal control strategy of a stochastic carbon emissions model.

Abstract

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 ϕ<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 ϖ>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.