Symbolic toolkit for chaos explorations

Abstract

Computational technique based on the symbolic description utilizing kneading invariants is proposed for explorations of parametric chaos in a two exemplary systems with the Lorenz attractor: a normal model from mathematics, and a laser model from nonlinear optics. The technique allows for uncovering the stunning complexity and universality of the patterns discovered in the bi-parametric scans of the given models and detects their organizing centers—codimension-two T-points and separating saddles.