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

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 $a_2$ (the driving coefficient of economic growth on carbon emissions) determines the threshold of state transition. With the increase in $a_2$, the system exhibits a clear evolutionary path from stable equilibrium to periodic state and then to chaotic state. The system enters chaos when $a_2$ 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.