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Criticality in conserved dynamical systems: Experimental observation vs. exact properties
Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for these routing models and governed by cyclic attractors. We consider two classes of information flow, Markovian routing without memory and vertex routing involving a one-step routing memory. Investigating the respective cycle length distributions for completedoi:10.1063/1.4773003 pmid:23556943 fatcat:b4nkg4roafeafknioqmczsxcfu