Resilience of finite clusters of carbon flux network under localized attack.

The investigation into the resilience of the carbon flux network regarding its capability to sustain the normal flow and transformation of carbon under extreme climatic events, pollutant emissions, biological invasions, and other factors, and the stability of connections between its nodes, has not yet been deeply studied. In this study, we developed carbon flux network models for various regional lands using complex networks, percolation theory, and introducing time delay effects using carbon flux daily data from 2000 to 2019 for three regions: China, the mainland United States, and Europe, to measure the resilience of finite clusters with sizes greater than or equal to s of the carbon flux network under localized attack. The analysis revealed that the carbon flux networks in different regions are characterized by a degree distribution consistent with the Poisson distribution. The carbon flux network demonstrated continuous phase transition behavior under localized attack. Interestingly, numerical simulation revealed a consistent relationship between the carbon flux network and the theoretical Erdős-Rényi network model. Moreover, the carbon flux network becomes more vulnerable as s increases. In addition, we discovered that there is a general scaling relationship of critical exponent δ≈-2 between the fraction of finite clusters and s. Therefore, investigating the resilience of carbon flux networks can enable us to predict and respond to the various risks and challenges, which will help policy designers formulate appropriate response strategies and enhance carbon flux systems' stability and resilience.