The Sequential Test for Chaos

TL;DR

This paper introduces a new numerical sequential test for detecting chaos in systems, complementing existing methods like Lyapunov exponents and bifurcation diagrams, with applications demonstrated on various systems.

Contribution

The paper presents a novel sequential testing method for chaos detection, providing explicit algorithms for both continuous and discrete systems, and demonstrating its effectiveness through theoretical and graphical examples.

Findings

Effective chaos detection in diverse systems

Complementary to Lyapunov and bifurcation methods

Validated with illustrative graphics

Abstract

This paper reveals a novel numerical method, the sequential test, which approves chaos through sequences of numbers observations. The method alights alongside the Lyapunov exponent and bifurcation diagram test. Explicitly elucidation of the method application for both continuous and discrete systemswas given affiliated with the corresponding algorithms. The theoretical results are exemplified on systems satisfying different types of definitions of chaos or numerical methods. The results are supplemented with illustrative graphics.