Anomalous Shattered Fragmentation Transition in the Coevolving Multiplex

We introduce a coevolution voter model in a multilayer, by coupling a fraction of nodes across two network layers and where each layer evolves according to its own temporal scale. For the symmetric case the dynamics preserve the absorbing-fragmentation transition observed in a monolayer network at a critical timescale that depends on interlayer connectivity. The time evolution equations obtained by pair approximation can be mapped to a coevolution voter model in a single layer with an effective average degree. In asymmetric settings, the fragmentation shows an anomalous transition with two large components in opposite states and the breakdown in many isolated nodes. We identify the growth of the number of components as a precursor of the shattered transitions.