In the process of Chinese economic development shifting from a stage of high-speed growth to a stage of high-quality development, carbon emissions caused by fossil energy consumption are also increasing. To reflect the interaction between Chinese carbon emissions from fossil energy consumption and economic growth, this paper constructed the fractional order cumulative multivariate gray model with equal-dimensional recursive optimization (EFMGM(1,2)) to predict the trend of carbon emissions from fossil energy consumption and constant price GDP in China and calculated the carbon emissions from fossil energy consumption according to the IPCC accounting method. EFMGM(1,2) is compared with other gray models to verify the performance of the model. The results show that this model has better prediction performance than other models. It can be used as an effective method for forecasting carbon emissions from fossil energy.

As we all know, it is difficult for traditional traffic models to deal with the phenomenon of “catastrophes” in traffic state and the traffic problem with incomplete information at the same time. Aiming at the traffic congestion, this paper firstly takes traffic volume as a state variable, speed, and density as control variables to establish the system potential function and theoretically clarifies that the structure of the traffic system has catastrophe characteristics. Secondly, combined with the grey characteristics of traffic system, we construct the grey catastrophe model for traffic system and obtain the traffic potential function with the system time as the state variable by substituting the variables of the model. Finally, the traffic stability is analyzed theoretically based on the potential function. In this paper, the rationality of the grey catastrophe model of traffic system is expounded theoretically, and the grey model theory is well expanded.