Kuehn Christian, Bick Christian
Faculty of Mathematics, Technical University of Munich, Garching, Germany.
Complexity Science Hub Vienna, Vienna, Austria.
Sci Adv. 2021 Apr 16;7(16). doi: 10.1126/sciadv.abe3824. Print 2021 Apr.
Critical transitions are observed in many complex systems. This includes the onset of synchronization in a network of coupled oscillators or the emergence of an epidemic state within a population. "Explosive" first-order transitions have caught particular attention in a variety of systems when classical models are generalized by incorporating additional effects. Here, we give a mathematical argument that the emergence of these first-order transitions is not surprising but rather a universally expected effect: Varying a classical model along a generic two-parameter family must lead to a change of the criticality. To illustrate our framework, we give three explicit examples of the effect in distinct physical systems: a model of adaptive epidemic dynamics, for a generalization of the Kuramoto model, and for a percolation transition.
在许多复杂系统中都观察到了临界转变。这包括耦合振子网络中同步的开始或人群中流行状态的出现。当通过纳入额外效应推广经典模型时，“爆发性”一阶转变在各种系统中引起了特别关注。在这里，我们给出一个数学论证，即这些一阶转变的出现并不奇怪，而是一种普遍预期的效应：沿着一个一般的双参数族改变经典模型必然会导致临界性的变化。为了说明我们的框架，我们给出了在不同物理系统中该效应的三个具体例子：自适应流行病动力学模型、Kuramoto模型的一种推广以及渗流转变。
