Publication detail

The Routh–Hurwitz conditions of fractional type in stability analysis of the Lorenz dynamical system

ČERMÁK, J. NECHVÁTAL, L.

Original Title

The Routh–Hurwitz conditions of fractional type in stability analysis of the Lorenz dynamical system

Type

journal article in Web of Science

Language

English

Original Abstract

This paper discusses stability conditions and a chaotic behavior of the Lorenz dynamical system involving the Caputo fractional derivative of orders between 0 and 1. We study these problems with respect to a general (not specified) value of the Rayleigh number as a varying control parameter. Such a bifurcation analysis is known for the classical Lorenz system; we show that analysis of its fractional extension can yield different conclusions. In particular, we theoretically derive (and numerically illustrate) that nontrivial equilibria of the fractional Lorenz system become locally asymptotically stable for all values of the Rayleigh number large enough, which contradicts the behavior known from the classical case. As a main proof tool, we derive the optimal Routh–Hurwitz conditions of fractional type. Beside it, we perform other bifurcation investigations of the fractional Lorenz system, especially those documenting its transition from stability to chaotic behavior.

Keywords

Fractional-order Lorenz dynamical system; Fractional Routh–Hurwitz conditions; Stability switch; Chaotic attractor

Authors

ČERMÁK, J.; NECHVÁTAL, L.

Released

12. 1. 2017

Publisher

Springer

Location

Dordrecht, Netherlands

ISBN

1573-269X

Periodical

NONLINEAR DYNAMICS

Year of study

87

Number

2

State

United States of America

Pages from

939

Pages to

954

Pages count

16

URL

https://link.springer.com/content/pdf/10.1007%2Fs11071-016-3090-9.pdf

BibTex

@article{BUT131305,
  author="Jan {Čermák} and Luděk {Nechvátal}",
  title="The Routh–Hurwitz conditions of fractional type in stability analysis of the Lorenz dynamical system",
  journal="NONLINEAR DYNAMICS",
  year="2017",
  volume="87",
  number="2",
  pages="939--954",
  doi="10.1007/s11071-016-3090-9",
  issn="1573-269X",
  url="https://link.springer.com/content/pdf/10.1007%2Fs11071-016-3090-9.pdf"
}