Hidden attractors and multistability in a modified Chua’s circuit

•Presents a modified Chua’s circuit with three stable node-foci and two unstable saddles.•Hidden attractors have very small attraction basins not being connected with any fixed point.•Hidden attractors coexist with point attractors in the entire period-doubling bifurcation route.•Circuit simulations...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2021-01, Vol.92, p.105494, Article 105494
Main Authors: Wang, Ning, Zhang, Guoshan, Kuznetsov, N.V., Bao, Han
Format: Article
Language:English
Subjects:
Attraction
Attraction basin
Attractors (mathematics)
Basins
Bifurcations
Chaos
Chaos theory
Chua’s circuit
Chua’s diode
Circuit design
Circuits
Diodes
Hidden attractor
Initial condition
Multistability
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Summary:•Presents a modified Chua’s circuit with three stable node-foci and two unstable saddles.•Hidden attractors have very small attraction basins not being connected with any fixed point.•Hidden attractors coexist with point attractors in the entire period-doubling bifurcation route.•Circuit simulations and DSP-assisted experiments validate the hidden attractors and multistability. The first hidden chaotic attractor was discovered in a dimensionless piecewise-linear Chua’s system with a special Chua’s diode. But designing such physical Chua’s circuit is a challenging task due to the distinct slopes of Chua’s diode. In this paper, a modified Chua’s circuit is implemented using a 5-segment piecewise-linear Chua’s diode. In particular, the coexisting phenomena of hidden attractors and three point attractors are noticed in the entire period-doubling bifurcation route. Attraction basins of different coexisting attractors are explored. It is demonstrated that the hidden attractors have very small basins of attraction not being connected with any fixed point. The PSIM circuit simulations and DSP-assisted experiments are presented to illustrate the existence of hidden attractors and coexisting attractors.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2020.105494