Abstract
In dimensional, homogeneous threshold models discontinuous transition occur, but the mean-field solution provides power-law activity decay and other power laws, and thus it is called mixed-order or hybrid type. It has recently been shown that the introduction of quenched disorder rounds the discontinuity and second-order phase transition and Griffiths phases appear. Here we provide numerical evidence that even in case of high graph dimensional hierarchical modular networks a Griffiths phase in the threshold model is present below the hybrid phase transition. This is due to the fragmentation of the activity propagation by modules, which are connected via single links. This provides a widespread mechanism in the case of the threshold type of heterogeneous systems, modeling the brain, or epidemics for the occurrence of dynamical criticality in extended Griffiths phase parameter spaces. We investigate this in synthetic modular networks with and without inhibitory links as well as in the presence of refractory states.
4 More- Received 2 December 2020
- Accepted 21 January 2021
DOI:https://doi.org/10.1103/PhysRevResearch.3.013106
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society