复杂网络上具有自适应行为的故障−恢复传播动力学研究

In the failure-recovery dynamics, nodes can recover spontaneously with probability after failure due to internal or external factors. Considering the ability of individual components to actively change their connectivity, we establish a failure-recovery propagation model on adaptive networks. In this model, active nodes disconnect from their failed neighbors to improve the local environment and thus reduce the probability of external failure. A theoretical framework based on pairwise approximation is established to predict the time evolution of the failure rate and the final failure size of the system. Numerous computer simulations validate the accuracy of the theoretical predictions and reveal the system’s rich phase transitions and hysteresis phenomena. Adaptive behavior can cause the hysteresis region of the system to appear or disappear under different adaptive edge-cutting rates and external failure rates, and the system exhibits a bistable region that is influenced by the initial failure size.