Carbon markets provide a market-based way to reduce climate pollution. Subject to general market regulations, the major existing emission trading markets present complex characteristics. This paper analyzes the complexity of carbon market by using the multi-scale entropy. Pilot carbon markets in China are taken as the example. Moving average is adopted to extract the scales due to the short length of the data set. Results show a low-level complexity inferring that China’s pilot carbon markets are quite immature in lack of market efficiency. However, the complexity varies in different time scales. China’s carbon markets (except for the Chongqing pilot) are more complex in the short period than in the long term. Furthermore, complexity level in most pilot markets increases as the markets developed, showing an improvement in market efficiency. All these results demonstrate that an effective carbon market is required for the full function of emission trading.

The carbon market is the least-cost tool to reduce carbon emissions. This study explores the evolution of the carbon price in the carbon market from a dynamic system perspective. A three-dimensional carbon price dynamic system is established to quantify the interactions among the carbon price, energy price, and economic growth. The system built in this study presents various dynamic characteristics including chaotic attractors and stable equilibria. Specifically, the existence of chaos in the system is verified by Lyapunov exponents spectrum and bifurcation diagram. In contrast, the system tends to be stable in the case of China after identifying the system parameters through the genetic algorithm. Furthermore, evolutionary trends of the carbon price are analyzed when the system parameters are perturbed. The results show that the carbon price is positively correlated with energy price as well as energy price policy. Besides, the level of the carbon price is negatively correlated with government control in the short term and positively correlated in the long term. This study can help analyze trends in the carbon price in the mid-term to long-term.