Numerical and experimental observation of Arnol’d resonance webs in an electrical circuit

Inaba, Nobuyuki; Kamiyama, Kyohei; Kousaka, Takuji; Endo, Tetsuro

doi:10.1016/j.physd.2015.08.008

Cited by 6 publications

(2 citation statements)

References 35 publications

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“…Дальнейшая эволюция области резонанса заключается в том, что внутренняя область хаоса расширяется и «влипает» в верхнюю границу устойчивости цикла. Чтобы проиллюстрировать возможность хаоса недостаточно бифуркационного анализа, поэтому представим ляпуновскую карту, построенную по методике [18][19][20]. В этом случае для ε = 0.675 на рис.…”

Section: бифуркационный анализ на пороге хаосаunclassified

Bifurcation analysis of the structure of complete synchronization of the system of non-identical Josephson junctions

Kuznetsov,

Sataev

2023

JRE

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The structure of the region of complete synchronization of a system of three connected Josephson junctions, non-identical in critical currents, was studied by the method of bifurcation analysis. On the plane of non-identity parameters, lines of saddle-node bifurcations, Neumark-Sacker bifurcations and period doublings were found, corresponding to a typical synchronization region. The influence of symmetry on the structure of the region of complete synchronization has been studied. In the system, under certain conditions, pitchfork bifurcation and associated bistability are possible. Bogdanov-Takens points, cusp points and fold-flip points are also indicated. The accumulation of points of the latter type is discussed based on cycles of doubling periods near the boundary of the synchronization and chaos regions.

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Section: бифуркационный анализ на пороге хаосаunclassified

Bifurcation analysis of the structure of complete synchronization of the system of non-identical Josephson junctions

Kuznetsov,

Sataev

2023

JRE

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“…Entrainment occurs when the two oscillation frequency components of two‐dimensional tori become rational, and these bifurcation structures and the bifurcation boundaries of the entrainment regions are called Arnol'd tongues. Arnol'd tongues have been observed in various physical oscillators such as forced , coupled , and autonomous oscillators . Kawakami presented general numerical methods for deriving the bifurcation boundaries of Arnol'd tongues for forced oscillators described by nonautonomous ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

Rigorous analysis of Arnol'd tongues from a manifold piecewise linear circuit

Tsubone

Inaba

2020

IEEJ Transactions Elec Engng

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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.

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