Alternative approaches of evaluating the 0–1 test for chaos

ABSTRACT

The 0–1 test for chaos is increasingly used in applications where it is important to distinguish between chaotic and regular dynamics of the deterministic dynamical system. This test consists of translating the time series into $(p,q)$ plane. Then the boundedness of the object created in the $(p,q)$ plane is inspected by computing mean square displacement and its growth rate. The computation of the mean square displacement for various lag has high computational complexity. In this paper, the inspection of the boundedness using bounding box and centre of gravity is proposed. This method has linear computational complexity and provides more control over the precision of the test through multiple input parameters.

KEYWORDS:

• 0–1 test for chaos
• dynamic systems
• time series
• computation
• mathematics

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 37M10
• 65P20

Acknowledgments

The authors would like to thank the anonymous referees for helpful comments that improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

T. Martinovič  http://orcid.org/0000-0002-0132-1434

Additional information

Funding

This work was supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) project ‘IT4Innovations excellence in science - LQ1602’.