On the Existence of the Double Scroll Attractor for the Chua's Circuit with a Smooth Nonlinearity

Zbigniew Galias, Warwick Tucker

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Abstract

In simulations of the Chua's circuit with a smooth nonlinearity for certain parameter values one observes the double scroll attractor. This attractor contains an unstable equilibrium, and typical trajectories belonging to the attractor may pass arbitrarily close to this equilibrium. In consequence, it is impossible to compute trajectories over the whole attractor using standard rigorous numerical integration procedures. This is due to the existence of trajectories which spend arbitrarily long time in a neighborhood of the equilibrium. In this work, a method to find enclosures of trajectories passing arbitrarily close to an unstable fixed point of spiral type is presented. This method is used to prove the existence of a trapping region enclosing the double scroll attractor for the Chua's circuit with a cubic nonlinearity.

Original languageEnglish
Title of host publicationProceedings - IEEE International Symposium on Circuits and Systems
Subtitle of host publication2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018; Florence; Italy; 27 May 2018 through 30 May 2018; Category number CFP18ISC-ART
Place of PublicationPiscataway NJ USA
PublisherIEEE, Institute of Electrical and Electronics Engineers
Number of pages5
ISBN (Electronic)9781538648810
DOIs
Publication statusPublished - 26 Apr 2018
Externally publishedYes
EventIEEE International Symposium on Circuits and Systems 2018 - Florence, Italy
Duration: 27 May 201830 May 2018
https://ieeexplore.ieee.org/xpl/conhome/8334884/proceeding (Proceedings)

Publication series

NameProceedings - IEEE International Symposium on Circuits and Systems
PublisherIEEE
Volume2018-May
ISSN (Print)0271-4310
ISSN (Electronic)2379-447X

Conference

ConferenceIEEE International Symposium on Circuits and Systems 2018
Abbreviated titleISCAS 2018
CountryItaly
CityFlorence
Period27/05/1830/05/18
Internet address

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