You are here: Home / Publications / Publications Database / Critical behaviors in contagion dynamics

Critical behaviors in contagion dynamics

Böttcher, L.; Nagler, J.; & Herrmann, H. J. (2017). Critical behaviors in contagion dynamics. Physical Review Letters, 118(8), 088301.

Böttcher, L.; Nagler, J.; & Herrmann, H. J. (2017). Critical behaviors in contagion dynamics. Physical Review Letters, 118(8), 088301.

Octet Stream icon 6852.ris — Octet Stream, 1 kB (1236 bytes)

We study the critical behavior of a general contagion model where nodes are either active (e.g. with opinion A, or functioning) or inactive (e.g. with opinion B, or damaged). The transitions between these two states are determined by (i) spontaneous transitions independent of the neighborhood, (ii) transitions induced by neighboring nodes and (iii) spontaneous reverse transitions. The resulting dynamics is extremely rich including limit cycles and random phase switching. We derive a unifying mean-field theory. Specifically, we analytically show that the critical behavior of systems whose dynamics is governed by processes (i-iii) can only exhibit three distinct regimes: (a) uncorrelated spontaneous transition dynamics (b) contact process dynamics and (c) cusp catastrophes. This ends a long-standing debate on the universality classes of complex contagion dynamics in mean-field and substantially deepens its mathematical understanding.




JOUR



Böttcher, L.
Nagler, J.
Herrmann, H. J.



2017


Physical Review Letters

118

8

088301










6852