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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/LO1202" target="_blank" >LO1202: NETME CENTRE PLUS</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

NONLINEAR DYNAMICS

ISSN

0924-090X

e-ISSN

1573-269X

Svazek periodika

87

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

939-954

Kód UT WoS článku

000392293200017

EID výsledku v databázi Scopus

2-s2.0-84991284340