Two-Parameter 0-1 Test for Chaos and Sample Entropy Bifurcation Diagrams for Nonlinear Oscillating Systems

Abstract

This paper presents and compares two-parameter bifurcation diagrams obtained from the 0-1 test for chaos and sample entropy methods for nonlinear oscillating systems. Based on the computed diagrams it is often possible to establish a unique correspondence between the two types of diagrams. Comparison of the diagrams are presented for typical chaotic systems, including those of Lorenz, Rössler, electric arc circuits and chemical oscillating systems. The two types of bifurcation diagrams may also be related to the period $-n$ and frequency distribution diagrams. The main goal is to address the issue of obtaining similar results from the 0-1 test for chaos and sample entropy methods and discuss difficulty in properly selecting parameters needed in the two methods. A possible link between the 0-1 test for chaos and surrogate data methods is also mentioned.

Keywords

• Time-series identification
• sample entropy
• the 0-1 test for chaos
• two-parameter bifurcation diagrams
• oscillatory nonlinear systems