Measuring and Locating Zones of Chaos and Irregularity by Application of High Spectral Chaotic Global Variants

Abstract

The protocol followed was analogous to that by Garner and Ling [2014]. High spectral Entropy and high spectral Detrended Fluctuation Analysis have been established as more sensitive to the chaotic responses in forward problems in subjects with type 1 diabetes mellitus (T1DM), chronic obstructive pulmonary disease (COPD), youth obesity and child malnutrition. From 50 linearly increasing starting points, we applied the objective functions (hsCTF1 to hsCTF7) to attain an optimized value, [Formula: see text] which should increase the chaotic response when substituted back into the appropriate model. The mean percentage increase in Kolmogorov–Sinai Entropy and [Formula: see text]-values when the models were compared statistically by Kruskal–Wallis and One-way analysis of variance (ANOVA1) tests were monitored. Normal distributions were considered by Anderson–Darling, Ryan–Joiner and Lilliefors tests. Effect sizes by Cohen’ [Formula: see text] and Hedges [Formula: see text] were computed as sometimes the ANOVA1 and Kruskal–Wallis tests were not discriminative. The optimal statistical results were Duffing (hsCTF1: 29.4%); Brusselator (hsCTF6: 24.7%); Lorenz (hsCTF6: 28.8%). Multivariate analysis was required to determine which of the seven combinations of chaotic globals were most influential. Following Principal Component Analysis (PCA) hsCTF1 and hsCTF3 were the preferred objective functions delivering the highest increases in mean KS-Entropy with most influential PCA. These methods could be advantageous to increase yields and consequently profits in industrial processes such as yeast glycolysis for alcoholic beverages, Systems Biology, inverse and optimization problems, generally.