双稳态传染动力学的老化与平衡
Aging and equilibration in bistable contagion dynamics
摘要：
我们分析了一般传染模型的晚期弛豫动力学。在这个模型中，节点要么是活动的，要么是故障的。活动节点可以在任何时候“自发地”失效，或者如果它们的邻居受到足够的破坏，则可以“外部地”失效。失败的节点总是可以自发地恢复。在晚期，时间平移不变性的打破是身体衰老的必要条件。我们观察到，时间平移不变性是失去了初始条件之间的盆地模型的两个稳定的定态的吸引力。基于相应的平均场预测，我们表征所观察到的模型行为的相图跨越自发和外部失败的节点的分数。对于正方形晶格，由于空间相关效应，动力学接近两个稳定定态之一的相位是不可线性分离的。我们的研究结果提供了新的见解老化和放松的现象，可观察到的社会传染过程的模型。
英文摘要：
We analyze the late-time relaxation dynamics for a general contagion model. In this model, nodes are either active or failed. Active nodes can fail either "spontaneously" at any time or "externally" if their neighborhoods are sufficiently damaged. Failed nodes may always recover spontaneously. At late times, the breaking of time-translation-invariance is a necessary condition for physical aging. We observe that time-translational invariance is lost for initial conditions that lie between the basins of attraction of the model's two stable stationary states. Based on corresponding mean-field predictions, we characterize the observed model behavior in terms of a phase diagram spanned by the fractions of spontaneously and externally failed nodes. For the square lattice, the phases in which the dynamics approaches one of the two stable stationary states are not linearly separable due to spatial correlation effects. Our results provide new insights into aging and relaxation phenomena that are observable in a model of social contagion processes.
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