Publication detail

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

ČERMÁK, J. NECHVÁTAL, L.

English title

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

Type

WoS Article

Language

en

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 in English

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

Released

2017-01-12

Publisher

Springer

Location

Dordrecht, Netherlands

ISSN

1573-269X

Volume

87

Number

2

Pages from–to

939–954

Pages count

16

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="0924-090X",
  url="https://link.springer.com/content/pdf/10.1007%2Fs11071-016-3090-9.pdf"
}