Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2011-07-04
Nonlinear Sciences
Adaptation and Self-Organizing Systems
5 pages
Scientific paper
It is a controversial question to which extend scaling is observed in critical dynamical systems. Here we examine a class of dynamical systems describing the propagation of conserved quantities, such as the routing of information packages, and which are designed as critical systems. The long term information flow is governed by properties of the cyclic attractors in phase space. We consider two classes of information routing models, Markovian routing without memory and vertex routing involving an one-step routing memory. Investigating the respective cycle length distributions for complete graphs we present analytic approximations which become exact in the limit of large numbers of vertices, the thermodynamic limit. We find log corrections to power-law scaling for the mean cycle length, as a function of the number of vertices, and a subpolynomial growth for the overall number of cycles.
Gros Claudius
Markovic Dimitrije
Schuelein Andre
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