Chaos Criteria Design Based on Modified Sign Functions with One or Three‐Threshold

Abstract

The complexity measures of chaotic or periodic signals are perpetual topics of interest to data scientists. This work adheres to the framework of the traditional 0-1 test for chaos and replaces sine and cosine functions by modified sign functions. The compressive mapping rules chosen are one-threshold of three-value or three-threshold of five-value. In new criteria for chaos in forms of the 3s plot and Ks metric compared with 0-1 test results, the periodic state of data features a short beeline instead of a big ring in the pq plot and signs the nearest zero mark, while the chaotic state signs a simple curve instead of a random-walking shape in the pq plot, and shows the nearest one mark. By computing the Lorenz equation evolution under the contrast tests of the Poincare section and Lyapunov index, we visualize a new chaoscriteria design in symbolic dynamics and data compression principles, and our work may lay the foundation for further expressing the chaotic appearance of novel signals deep into future brainets.