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On the Existence of the Double Scroll Attractor for the Chua's Circuit with a Smooth Nonlinearity
AGH Univ Sci & Technol, Dept Elect Engn, Al Mickiewicza 30, PL-30059 Krakow, Poland.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
2018 (English)In: 2018 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS (ISCAS), IEEE , 2018Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
IEEE , 2018.
Series
IEEE International Symposium on Circuits and Systems, ISSN 0271-4302
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-372523DOI: 10.1109/ISCAS.2018.8351549ISI: 000451218703015ISBN: 978-1-5386-4881-0 (print)OAI: oai:DiVA.org:uu-372523DiVA, id: diva2:1276693
Conference
IEEE International Symposium on Circuits and Systems (ISCAS), MAY 27-30, 2018, Florence, ITALY
Available from: 2019-01-08 Created: 2019-01-08 Last updated: 2019-01-08Bibliographically approved

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