Heterogeneous excitable systems exhibit Griffiths phases below hybrid phase transitions

In d>2 dimensional, homogeneous threshold models discontinuous transition occur, but the mean-field solution provides 1/t power-law activity decay and other power laws, thus it is called mixed-order or hybrid type. It has recently been shown that introduction of quenched disorder rounds discontinuity second-order phase Griffiths phases appear. Here we provide numerical evidence even in case high graph dimensional hierarchical modular networks a K=2 model present below transition. This due to fragmentation propagation by modules, which are connected via single links. widespread mechanism type heterogeneous systems, modeling brain, epidemics for occurrence dynamical criticality extended parameter spaces. We investigate this synthetic with without inhibitory links as well presence refractory states.4 MoreReceived 2 December 2020Accepted 21 January 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013106Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasCritical phenomenaDynamical transitionsNonequilibrium statistical mechanicsPhysical SystemsDisordered systemsNetworks & random structuresNonequilibrium lattice modelsStatistical Physics