AUTHOR=Zhao Hongkun , Chen Qishen , Zhang Yanfei , Wang Kun , Shao Liuguo , Shang Chenghong , Zhang Hua , Zhang Ye , Song Dan 
  
TITLE=Features of Chinese copper future return: based on a markov network approach
  
JOURNAL=Frontiers in Physics
  
VOLUME=Volume 13 - 2025
  
YEAR=2025
  
URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2025.1713083
  
DOI=10.3389/fphy.2025.1713083
  
ISSN=2296-424X
  
ABSTRACT=IntroductionCopper has the dual attributes of industrial raw materials and financial assets, and its price formation mechanism presents complex non-linear characteristics under the dual role of supply and demand mechanism and financialization. The structural upgrading of industrial demand and the risk contagion effect in the futures market make it difficult to effectively analyze the fluctuation characteristics of copper price in the traditional linear analytical framework. Consequently, it is significant to explore the fluctuation characteristics of copper futures price from the perspective of complex system science.MethodsThis study employed complex network theory and the Markov switching model to develop a Markov network model of copper futures and to explore the evolving characteristics of copper prices.Results and discussionThis study finds that: (1) There are 243 price switch states in theory, but only 126 types of states actually occur. Among them, 33 high-frequency states account for 90% of the total number of times, indicating that price fluctuations are active and concentrated in a regular manner. (2) The average path length of network state transition is 5.4, and the symmetry coefficient is 0.99, which shows that the transition efficiency is high but the path is highly asymmetric. (3) There are some nodes with low degree centrality and high betweenness centrality in the network, which act as mediators in the network, connecting the transitions between states. (4) The network has a significant association structure, and we find that the state nodes have a relatively obvious “rich club” effect. This study reveals that the nonlinear dynamics and network structures of copper future return.