复杂网络上具有自适应行为的故障-恢复传播动力学研究

The Failure-Recovery Propagation Dynamics with Adaptive Behavior in Complex Networks

在故障-恢复动力学中,节点受内部或外部因素而故障失效后能够有概率自发恢复。考虑到未故障的节点存在避免故障的自适应行为,建立自适应网络上的故障-恢复传播模型。在该模型中,活跃节点为了改善自身局域环境以降低外部故障概率,将主动断开与故障邻居的连边,直到故障邻居恢复正常工作后再重新建立连接。基于点对近似思想建立了理论框架,用于预测故障率的时间演化趋势和系统的最终故障规模。大量的计算机仿真结果验证了理论预测的准确性,并发现系统具有相变和磁滞现象。在不同的自适应断边速率和外部故障速率下,自适应行为能使系统的磁滞区域产生或消失,系统将出现受初始故障规模影响的双稳态区域。

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.