Chaos Detection with Persistent Homology

This data set contains MATLAB scripts which generate a Persistence Score (PS) for a time series. The time series are generated from dynamical systems (specifically the Lorenz model, Rossler model, and Logistics map) across an array of bifurcation parameters. The PS scores are generated from a persistence diagram which is taken of a bi-variate kernel density estimate of a planar projection of the time series data. This library contains MATLAB data structures which store the results several studies of the PS scores. Specifically, results are included which span a bifurcation of the Rossler, Logistics, and Lorenz models. The same results are given in separate data structures for time-series with added White Gaussian noise. The PS scores are computed along with 0/1 scores, and these scoring systems are compared. A MALTAB file (Scoring.m) unpacks and plots the results of this study. A Gaussian smoothing function is used in this study to condition gray scale images in preparation for persistent homology. The effect of th kernel width sigma on the PS scores is studied, and MATLAB data structures are included which contain the results of this study for clean data along with data contaminated with noise at an Signal to Noise Ratio of 30 dB over a span of sigma = 0.1 to sigma 4.0.