Exact solution of a class of critical dynamical systems: Information routing in complete graphs
Year: 2011
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W61504304