Absorbing transition in a coevolution model with node and link states in an adaptive network: Network fragmentation transition at criticality

Saeedian, Meghdad; San Miguel, Maxi; Toral, Raul
Submitted (2020)

We consider a general model in which there is a coupled dynamics of node
states and links states in a network. This coupled dynamics coevolves with dynamical
changes of the topology of the network caused by a link rewiring mechanism. Such
coevolution model features the interaction of the local dynamics of node and link
states with the nonlocal dynamics of link-rewiring in a random network. The coupled
dynamics of the states of the nodes and the links produces by itself an absorbing phase
transition which is shown to be robust against the link rewiring mechanism. However,
the dynamics of the network gives rise to significant physical changes, specially in the
limit in which some links do not change state but are always rewired: First a network
fragmentation occurs at the critical line of the absorbing transition, and only at this
line, so that fragmentation is a manifestation of criticality. Secondly, in the active
phase of the absorbing transition, finite-size fluctuations take the system to a single
network component consensus phase, while other configurations are possible in the
absence of rewiring. In addition, this phase is reached after a survival time that scales
linearly with system size, while the survival time scales exponentially with system size
when there is no rewiring. A social interpretation of our results contribute to the
description of processes of emergence of social fragmentation and polarization.

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