The Routh–Hurwitz conditions of fractional type in stability analysis of the Lorenz dynamical system
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F17%3APU121833" target="_blank" >RIV/00216305:26210/17:PU121833 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/content/pdf/10.1007%2Fs11071-016-3090-9.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007%2Fs11071-016-3090-9.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11071-016-3090-9" target="_blank" >10.1007/s11071-016-3090-9</a>
Alternative languages
Result language
angličtina
Original language name
The Routh–Hurwitz conditions of fractional type in stability analysis of the Lorenz dynamical system
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/LO1202" target="_blank" >LO1202: NETME CENTRE PLUS</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
NONLINEAR DYNAMICS
ISSN
0924-090X
e-ISSN
1573-269X
Volume of the periodical
87
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
939-954
UT code for WoS article
000392293200017
EID of the result in the Scopus database
2-s2.0-84991284340