DYNAMIC MODELING OF CARBON DIOXIDE EMISSIONS USING HIGH-ORDER DIFFERENTIAL EQUATIONS AND NONLINEAR ESTIMATION

Abstract

Carbon dioxide (CO₂) is one of the main factors contributing to global warming. As the second largest CO₂ emitter globally, the United States (US) faces increasing political and economic pressure to reduce its emissions. Historical emission data exhibits complex structural patterns characterized by linear growth, quadratic trends, and periodic oscillations. Most existing models fail to capture this multifaceted behavior. In this study, we propose a high-order differential equation to represent the dynamic behavior of CO₂ emissions in the US. The model integrates linear, quadratic, and oscillatory components to reflect both long-term and short-term fluctuations. Nonlinear parameter estimation techniques are employed to fit the model to historical emission data with high accuracy. The proposed model effectively captures historical emission behavior, demonstrating strong goodness of fit and identifying both trend and cyclical components. Model-based projections indicate a likely resurgence in emission growth over the next decade, raising concerns regarding compliance with climate commitments and potential exposure to international carbon pricing instruments. The findings highlight the value of combining differential equation modeling with nonlinear estimation in analyzing environmental systems. The main limitation of this study is that it focuses only on historical emission dynamics, without direct integration of socio-economic drivers. This gap, however, highlights opportunities for future research.