On the existence of the double scroll attractor for the Chua's circuit with a smooth nonlinearity

Zbigniew Galias; Warwick Tucker

doi:10.1109/ISCAS.2018.8351549

On the existence of the double scroll attractor for the Chua's circuit with a smooth nonlinearity

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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 language	English
Title of host publication	Proceedings - IEEE International Symposium on Circuits and Systems
Subtitle of host publication	2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018; Florence; Italy; 27 May 2018 through 30 May 2018; Category number CFP18ISC-ART
Place of Publication	Piscataway NJ USA
Publisher	IEEE, Institute of Electrical and Electronics Engineers
Pages	4268-4272
Number of pages	5
ISBN (Electronic)	9781538648810
DOIs	https://doi.org/10.1109/ISCAS.2018.8351549
Publication status	Published - 26 Apr 2018
Externally published	Yes
Event	IEEE International Symposium on Circuits and Systems 2018 - Florence, Italy Duration: 27 May 2018 → 30 May 2018 https://ieeexplore.ieee.org/xpl/conhome/8334884/proceeding (Proceedings)

Publication series

Name	Proceedings - IEEE International Symposium on Circuits and Systems
Publisher	IEEE
Volume	2018-May
ISSN (Print)	0271-4310
ISSN (Electronic)	2379-447X

Conference

Conference	IEEE International Symposium on Circuits and Systems 2018
Abbreviated title	ISCAS 2018
Country/Territory	Italy
City	Florence
Period	27/05/18 → 30/05/18
Internet address	https://ieeexplore.ieee.org/xpl/conhome/8334884/proceeding (Proceedings)

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10.1109/ISCAS.2018.8351549

Cite this

Galias, Z., & Tucker, W. (2018). On the existence of the double scroll attractor for the Chua's circuit with a smooth nonlinearity. In Proceedings - IEEE International Symposium on Circuits and Systems: 2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018; Florence; Italy; 27 May 2018 through 30 May 2018; Category number CFP18ISC-ART (pp. 4268-4272). (Proceedings - IEEE International Symposium on Circuits and Systems; Vol. 2018-May). IEEE, Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISCAS.2018.8351549

Galias, Zbigniew ; Tucker, Warwick. / On the existence of the double scroll attractor for the Chua's circuit with a smooth nonlinearity. Proceedings - IEEE International Symposium on Circuits and Systems: 2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018; Florence; Italy; 27 May 2018 through 30 May 2018; Category number CFP18ISC-ART. Piscataway NJ USA : IEEE, Institute of Electrical and Electronics Engineers, 2018. pp. 4268-4272 (Proceedings - IEEE International Symposium on Circuits and Systems).

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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.",

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Galias, Z & Tucker, W 2018, On the existence of the double scroll attractor for the Chua's circuit with a smooth nonlinearity. in Proceedings - IEEE International Symposium on Circuits and Systems: 2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018; Florence; Italy; 27 May 2018 through 30 May 2018; Category number CFP18ISC-ART. Proceedings - IEEE International Symposium on Circuits and Systems, vol. 2018-May, IEEE, Institute of Electrical and Electronics Engineers, Piscataway NJ USA, pp. 4268-4272, IEEE International Symposium on Circuits and Systems 2018, Florence, Italy, 27/05/18. https://doi.org/10.1109/ISCAS.2018.8351549

On the existence of the double scroll attractor for the Chua's circuit with a smooth nonlinearity. / Galias, Zbigniew; Tucker, Warwick.
Proceedings - IEEE International Symposium on Circuits and Systems: 2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018; Florence; Italy; 27 May 2018 through 30 May 2018; Category number CFP18ISC-ART. Piscataway NJ USA: IEEE, Institute of Electrical and Electronics Engineers, 2018. p. 4268-4272 (Proceedings - IEEE International Symposium on Circuits and Systems; Vol. 2018-May).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

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N2 - 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.

AB - 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.

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Galias Z, Tucker W. On the existence of the double scroll attractor for the Chua's circuit with a smooth nonlinearity. In Proceedings - IEEE International Symposium on Circuits and Systems: 2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018; Florence; Italy; 27 May 2018 through 30 May 2018; Category number CFP18ISC-ART. Piscataway NJ USA: IEEE, Institute of Electrical and Electronics Engineers. 2018. p. 4268-4272. (Proceedings - IEEE International Symposium on Circuits and Systems). doi: 10.1109/ISCAS.2018.8351549

On the existence of the double scroll attractor for the Chua's circuit with a smooth nonlinearity

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