Resonant regions of Josephson junction equation in case of large damping

Qian, Min; Wang, Jia-Zeng; Zhang, Xuejuan

doi:10.1016/j.physleta.2008.02.029

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…a self-similar fractal object, where the qualitative structure is replicated at a higher level of resolution, with plateaux corresponding to rational values of the ratio. The phase locking phenomenon, the existence of the Arnold tongues, and the devil's staircase picture have been proved rigorously in some mathematical models, such as the circle map (Arnold 1988), and studied numerically for several electronic circuits, such as the van der Pol equation (Guckenheimer & Holmes 1990), the Josephson junction (Abidi & Chua 1979;Levi 1988;Qian et al 2008), the Chua circuit (Pivka et al 1994) among others.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

“…The phase locking phenomenon, the existence of the Arnold tongues, and the devil's staircase picture have been proved rigorously in some mathematical models, such as the circle map [2], and studied numerically for several electronic circuits, such as the van der Pol equation [18], the Josephson junction [1,23,30], the Chua circuit [29] among others.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

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Frequency locking in an injection-locked frequency divider equation

2008

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We consider a model for a resonant injection-locked frequency divider, and study analytically the locking onto rational multiples of the driving frequency. We provide explicit formulae for the width of the plateaux appearing in the devil's staircase structure of the lockings, and in particular show that the largest plateaux correspond to even integer values for the ratio of the frequency of the driving signal to the frequency of the output signal. Our results prove the experimental and numerical results available in the literature.

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Section: Conclusion and Open Problemsmentioning

confidence: 99%

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Frequency locking in an injection-locked frequency divider equation

2008

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“…The frequency locking phenomenon, the existence of the Arnol ′ d tongues, and the devil's staircase structure have been proved rigorously in some mathematical models, such as the circle map [3], and studied numerically or experimentally for several electronic circuits, such as the van der Pol equation [9,17], the Josephson junction [1,13,20], the Chua circuit [18] among others.…”

Section: Introductionmentioning

confidence: 99%

Arnol’d tongues for a resonant injection-locked frequency divider: Analytical and numerical results

Bartuccelli

Deane

Gentile

et al. 2010

Nonlinear Analysis: Real World Applications

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In this paper we consider a resonant injection-locked frequency divider which is of interest in electronics, and we investigate the frequency locking phenomenon when varying the amplitude and frequency of the injected signal. We study both analytically and numerically the structure of the Arnol ′ d tongues in the frequency-amplitude plane. In particular, we provide exact analytical formulae for the widths of the tongues, which correspond to the plateaux of the devil's staircase picture. The results account for numerical and experimental findings presented in the literature for special driving terms and, additionally, extend the analysis to a more general setting.

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Bursting behaviour in coupled Josephson junctions

Hongray

Balakrishnan

Dana

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We report an interesting bow-tie shaped bursting behaviour in a certain parameter regime of two resistive-capacitative shunted Josephson junctions, one in the oscillatory and the other in the excitable mode and coupled together resistively. The burst emerges in both the junctions and they show near-complete synchronization for strong enough couplings. We discuss a possible bifurcation scenario to explain the origin of the burst. An exhaustive study on the parameter space of the system is performed, demarcating the regions of bursting from other solutions.

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Resonant regions of Josephson junction equation in case of large damping

Cited by 3 publications

References 19 publications

Frequency locking in an injection-locked frequency divider equation

Frequency locking in an injection-locked frequency divider equation

Arnol’d tongues for a resonant injection-locked frequency divider: Analytical and numerical results

Bursting behaviour in coupled Josephson junctions

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