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arXiv · 2002.10714

A Universal Route to Explosive Phenomena

Christian Kuehn·Christian Bick
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Abstract

Critical transitions are observed in many complex systems. This includes the onset of synchronization in a network of coupled oscillators or the emergence 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 such 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.

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Christian Kuehn, Christian Bick. 2020-02-25. A Universal Route to Explosive Phenomena. https://doi.org/10.1126/sciadv.abe3824

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