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

Galias, ZbigniewAGH Univ Sci & Technol, Dept Elect Engn, Al Mickiewicza 30, PL-30059 Krakow, Poland (author)

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.

Tucker, Warwick,1970-Uppsala universitet,Tillämpad matematik och statistik(Swepub:uu)watuc425 (author)
AGH Univ Sci & Technol, Dept Elect Engn, Al Mickiewicza 30, PL-30059 Krakow, PolandTillämpad matematik och statistik (creator_code:org_t)

In:2018 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS (ISCAS): IEEE9781538648810

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NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Computational Ma ...

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