Publication detail

Local Bifurcations and Chaos in the Fractional Rössler System

ČERMÁK, J. NECHVÁTAL, L.

Original Title

Local Bifurcations and Chaos in the Fractional Rössler System

English Title

Local Bifurcations and Chaos in the Fractional Rössler System

Type

journal article in Web of Science

Language

en

Original Abstract

The paper discusses the fractional Rössler system and the dependence of its dynamics on some entry parameters. An explicit algorithm for a priori determination of fractional Hopf bifurcations is derived and scenarios documenting a route of the system from stability to chaos are performed with respect to a varying system’s fractional order as well as to a varying system’s coefficient. Contrary to the existing results, the searched values of the fractional Hopf bifurcations follow directly from a revealed analytical dependence between these two systems’ entries.

English abstract

The paper discusses the fractional Rössler system and the dependence of its dynamics on some entry parameters. An explicit algorithm for a priori determination of fractional Hopf bifurcations is derived and scenarios documenting a route of the system from stability to chaos are performed with respect to a varying system’s fractional order as well as to a varying system’s coefficient. Contrary to the existing results, the searched values of the fractional Hopf bifurcations follow directly from a revealed analytical dependence between these two systems’ entries.

Keywords

Rössler dynamical system; fractional derivative; asymptotic stability; fractional Hopf bifurcation; chaos synchronization

Released

01.07.2018

Publisher

World Scientific Publishing Co. Pte Ltd

Location

Singapore

Pages from

1850098-1

Pages to

1850098-17

Pages count

17

URL

BibTex


@article{BUT152948,
  author="Jan {Čermák} and Luděk {Nechvátal}",
  title="Local Bifurcations and Chaos in the Fractional Rössler System",
  annote="The paper discusses the fractional Rössler system and the dependence of its dynamics on some entry parameters. An explicit algorithm for a priori determination of fractional Hopf bifurcations is derived and scenarios documenting a route of the system from stability to chaos are performed with respect to a varying system’s fractional order as well as to a varying system’s coefficient. Contrary to the existing results, the searched values of the fractional Hopf bifurcations follow directly from a revealed analytical dependence between these two systems’ entries.",
  address="World Scientific Publishing Co. Pte Ltd",
  chapter="152948",
  doi="10.1142/S0218127418500980",
  howpublished="print",
  institution="World Scientific Publishing Co. Pte Ltd",
  number="8",
  volume="28",
  year="2018",
  month="july",
  pages="1850098-1--1850098-17",
  publisher="World Scientific Publishing Co. Pte Ltd",
  type="journal article in Web of Science"
}