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Article

Construction and Application of a Dynamic Model Integrating Technological Progress, Carbon Emissions, Economic Growth, and Energy Structure

1
School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China
2
Department of Mathematics, Nanjing Normal University Taizhou College, Taizhou 225300, China
3
Ministry of Education Key Laboratory of NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(9), 1575; https://doi.org/10.3390/math14091575
Submission received: 2 April 2026 / Revised: 1 May 2026 / Accepted: 4 May 2026 / Published: 6 May 2026

Abstract

Technological progress reduces carbon emissions by promoting energy structure optimization while fostering new industries and improving efficiency, thus achieving a win–win situation for economic growth and low-carbon development. From the perspective of mechanism analysis, this paper constructs a new dynamic system model of technological progress–carbon emissions–economic growth–energy structure based on the interdependent and mutually restrictive causal relationships among technological progress, carbon emissions, economic growth and energy structure within an economic period. The dynamical behaviors of the system and its subsystems are analyzed using Lyapunov exponents, bifurcation diagrams, equilibrium point stability theory and other methods. Numerical simulations show that the system parameter a2 (the driving coefficient of economic growth on carbon emissions) determines the threshold of state transition. With the increase in a2, the system exhibits a clear evolutionary path from stable equilibrium to periodic state and then to chaotic state. The system enters chaos when a2 falls within the interval [0.741, 0.79]. Model parameters are estimated based on real data, the evolutionary relationships of technological progress, carbon emissions, energy structure and economic growth over time are presented, and the impacts of different regulation strategies on carbon emission reduction and economic growth are analyzed.
Keywords: nonlinear dynamic system; equilibrium point theory; numerical simulation; energy economics nonlinear dynamic system; equilibrium point theory; numerical simulation; energy economics

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MDPI and ACS Style

Wang, X.; Xu, H.; Song, Y.; Sheng, Z.; Wang, M. Construction and Application of a Dynamic Model Integrating Technological Progress, Carbon Emissions, Economic Growth, and Energy Structure. Mathematics 2026, 14, 1575. https://doi.org/10.3390/math14091575

AMA Style

Wang X, Xu H, Song Y, Sheng Z, Wang M. Construction and Application of a Dynamic Model Integrating Technological Progress, Carbon Emissions, Economic Growth, and Energy Structure. Mathematics. 2026; 14(9):1575. https://doi.org/10.3390/math14091575

Chicago/Turabian Style

Wang, Xiongfei, Hua Xu, Yuanyuan Song, Zhirong Sheng, and Minggang Wang. 2026. "Construction and Application of a Dynamic Model Integrating Technological Progress, Carbon Emissions, Economic Growth, and Energy Structure" Mathematics 14, no. 9: 1575. https://doi.org/10.3390/math14091575

APA Style

Wang, X., Xu, H., Song, Y., Sheng, Z., & Wang, M. (2026). Construction and Application of a Dynamic Model Integrating Technological Progress, Carbon Emissions, Economic Growth, and Energy Structure. Mathematics, 14(9), 1575. https://doi.org/10.3390/math14091575

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