Detail publikace
The Routh–Hurwitz conditions of fractional type in stability analysis of the Lorenz dynamical system
ČERMÁK, J. NECHVÁTAL, L.
Anglický název
The Routh–Hurwitz conditions of fractional type in stability analysis of the Lorenz dynamical system
Typ
Článek WoS
Jazyk
en
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 anglicky
Fractional-order Lorenz dynamical system; Fractional Routh–Hurwitz conditions; Stability switch; Chaotic attractor
Vydáno
2017-01-12
Nakladatel
Springer
Místo
Dordrecht, Netherlands
ISSN
1573-269X
Časopis
NONLINEAR DYNAMICS
Ročník
87
Číslo
2
Strany od–do
939–954
Počet stran
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"
}