Grid-based partitioning for comparing attractors.

Abstract

Stationary dynamical systems have invariant measures (or densities) that are characteristic of the particular dynamical system. We develop a method to characterize this density by partitioning the attractor into the smallest regions in phase space that contain information about the structure of the attractor. To accomplish this, we develop a statistic that tells us if we get more information about our data by dividing a set of data points into partitions rather than just lumping all the points together. We use this method to show that not only can we detect small changes in an attractor from a circuit experiment, but we can also distinguish between a large set of numerically generated chaotic attractors designed by Sprott. These comparisons are not limited to chaotic attractors-they should work for signals from any finite-dimensional dynamical system.