Boundary transformation representation of attractor shape deformation.

Abstract

Detecting parameter changes in chaotic systems depends on characterizing the deformation of the strange attractor. Here, we present a new method for comparing the geometry of two attractors by examining their boundaries in 2D via shape context analysis. Poincaré sections for each attractor are sampled along their outer limits, and a boundary transformation is computed that warps one set of points into the other. This boundary transformation is a rich descriptor of the attractor deformation and approximately proportional to a system parameter change in specific regions. Both simulated and experimental data with various levels of noise are used to demonstrate the effectiveness of this method.