Publication detail

Chaotic systems based on higher-order oscillatory equations

PETRŽELA, J.

Original Title

Chaotic systems based on higher-order oscillatory equations

Type

journal article in Web of Science

Language

English

Original Abstract

This paper discusses the design process toward new lumped chaotic systems that originates in higher‑order ordinary differential equations commonly used as description of ideal oscillators. In investigated third‑order case, two chaotic oscillators were constructed. These systems are dual in the sense of vector field geometry local to fixed points. The existence of robust chaos was proved by both standard routines of numerical analysis and practical measurement. For the fourth‑order oscillatory equation, the concept based on interaction between superinductor and supercapacitor was examined in detail. Since both “superelements” are active, the nonlinearity essential to the evolution of chaos is fully passive. It is demonstrated that complex motion is robust and does not represent long transient behavior or numerical artefact. The existence of chaos was verified using standard quantifiers of the flow, such as the largest Lyapunov exponents, recurrence plots, approximate entropy and sensitivity calculation. A good final agreement between theoretical assumptions and practical results will be concluded, on a visual comparison basis.

Keywords

Chaos; chaotic system; oscillatory equation; strange attractor

Authors

PETRŽELA, J.

Released

10. 9. 2024

Publisher

NATURE PORTFOLIO

Location

HEIDELBERGER PLATZ 3, BERLIN 14197, GERMANY

ISBN

2045-2322

Periodical

Scientific Reports

Year of study

14

Number

1

State

United Kingdom of Great Britain and Northern Ireland

Pages from

21075

Pages to

21095

Pages count

21

URL

https://www.nature.com/articles/s41598-024-72034-6

Full text in the Digital Library

http://hdl.handle.net/11012/249484

BibTex

@article{BUT189607,
  author="Jiří {Petržela}",
  title="Chaotic systems based on higher-order oscillatory equations",
  journal="Scientific Reports",
  year="2024",
  volume="14",
  number="1",
  pages="21075--21095",
  doi="10.1038/s41598-024-72034-6",
  issn="2045-2322",
  url="https://www.nature.com/articles/s41598-024-72034-6"
}