Statistically relaxing to generating partitions for observed time-series data.
We introduce a relaxation algorithm to estimate approximations to generating partitions for observed dynamical time series. Generating partitions preserve dynamical information of a deterministic map in the symbolic representation. Our method optimizes an essential property of a generating partition: avoiding topological degeneracies. We construct an energy-like functional and use a nonequilibrium stochastic minimization algorithm to search through configuration space for the best assignment of symbols to observed data. As each observed point may be assigned a symbol, the partitions are not constrained to an arbitrary parametrization. We further show how to select particular generating partition solutions which also code low-order unstable periodic orbits in a given way, hence being able to enumerate through a number of potential generating partition solutions.
Buhl
Michael
M
Institute For Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402, USA. mbuhl@clack.ucsd.edu
Kennel
Matthew B
MB