Detail publikace

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

ČERMÁK, J. NECHVÁTAL, L.

Originální název

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

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

ČERMÁK, J.; NECHVÁTAL, L.

Vydáno

12. 1. 2017

Nakladatel

Springer

Místo

Dordrecht, Netherlands

ISSN

1573-269X

Periodikum

NONLINEAR DYNAMICS

Ročník

87

Číslo

2

Stát

Spojené státy americké

Strany od

939

Strany do

954

Strany počet

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"
}