HR: 09:00h
AN: NG21A-05 INVITED     [Abstracts]
TI: Quantifying Self-Organization and Coherent Structures with Statistical Complexity
AU: * Shalizi, C R
EM: cshalizi@umich.edu
AF: Center for the Study of Complex Systems, University of Michigan, 4485 Randall Laboratory 500 East University, Ann Arbor, MI 48109 United States
AB: Despite broad interest in self-organizing systems, there are few quantitative criteria for self-organization which can be applied to dynamical models, let alone experimental data. The existing criteria all give counter-intuitive results in important cases. A resolution is offered by a recently-proposed criterion, namely an internally-generated increase in the statistical complexity, the amount of information required for optimal prediction of the system's dynamics. This complexity can be precisely defined for spatially-extended dynamical systems, using the probabilistic ideas of mutual information and minimal sufficient statistics. The definition also leads to a general method for predicting such systems, and a simple algorithm for estimating statistical complexity. Examining the variation in the statistical complexity over space and time provides a way of automatically identifying the coherent structures generated by the system. The results of applying this algorithm to two important classes of cellular automata (CA) --- cyclic CA, which model excitable media, and sandpile CA, which are prototypes of self-organized criticality --- illustrate the general ideas.
UR: http://bactra.org/research/
DE: 3220 Nonlinear dynamics
DE: 3240 Chaos
SC: Nonlinear Geophysics [NG]
MN: 2004 AGU Fall Meeting