论文标题
外部字段和关键指数控制复杂网络上的动态
External field and critical exponents in controlling dynamics on complex networks
论文作者
论文摘要
复杂网络上的动力学过程，从生物，技术和社会系统范围内显示了系统的不同全球状态之间的相变。通常，这种过渡依赖于发生在其上发生的结构和动力学之间的相互作用，因此弱连接性（稀疏网络或脆弱的相互作用）可能导致全球活动崩溃，而强大的连通性会导致高活动。在这里，我们表明，在此类系统中，控制一部分节点的动力学在连续的相变中充当外部场。因此，它在平衡时间和瞬态时间定义了相应的临界指数。我们使用动态函数的领先顺序找到了通用动力类别的关键指数。通过将此框架应用于三个示例，我们揭示了不同的普遍性类别。
Dynamical processes on complex networks, ranging from biological, technological and social systems, show phase transitions between distinct global states of the system. Often, such transitions rely upon the interplay between the structure and dynamics that takes place on it, such that weak connectivity, either sparse network or frail interactions, might lead to global activity collapse, while strong connectivity leads to high activity. Here, we show that controlling dynamics of a fraction of the nodes in such systems acts as an external field in a continuous phase transition. As such, it defines corresponding critical exponents, both at equilibrium and of the transient time. We find the critical exponents for a general class of dynamics using the leading orders of the dynamic functions. By applying this framework to three examples, we reveal distinct universality classes.
