Detail publikačního výsledku

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

Anglický název

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

Druh

Článek WoS

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.

Anglický 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

Klíčová slova v angličtině

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

Autoři

ČERMÁK, J.; NECHVÁTAL, L.

Rok RIV

2018

Vydáno

12.01.2017

Nakladatel

Springer

Místo

Dordrecht, Netherlands

ISSN

1573-269X

Periodikum

NONLINEAR DYNAMICS

Svazek

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

Dokumenty

Čermák-Nechvátal2017_Article_TheRouthHurwitzConditionsOfFra