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- Title
Rigorous analysis of Arnol'd tongues from a manifold piecewise linear circuit.
- Authors
Le, Viet Duc; Tsubone, Tadashi; Inaba, Naohiko
- Abstract
This report presents rigorous analysis of Arnol'd tongues generated by a manifold piecewise linear circuit. The circuit comprises an LC oscillator, a conductive switch that produces the manifold, and a voltage source controlled by the current value through the inductor when the voltage across the capacitor exceeds a threshold. From the circuit dynamics, the Poincaré return map is explicitly derived as a piecewise linear circle map, and the generation of Arnol'd tongues is precisely explained. We attempt to derive the border–collision bifurcation boundaries of the Arnol'd tongues, some of which are obtained explicitly. Furthermore, we experimentally verify these theoretical results. © 2020 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.
- Subjects
JAPAN; JOHN Wiley &; Sons Inc.; LOCUS coeruleus; LINEAR operators; IDEAL sources (Electric circuits); VOLTAGE control; MANIFOLDS (Mathematics)
- Publication
IEEJ Transactions on Electrical & Electronic Engineering, 2020, Vol 15, Issue 7, p1070
- ISSN
1931-4973
- Publication type
Article
- DOI
10.1002/tee.23152