Chaos and noise rise in Josephson junctions

Pedersen, Niels Falsig; Davidson, A.

doi:10.1063/1.92574

Cited by 141 publications

(20 citation statements)

References 3 publications

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“…It was also shown that the onset of chaos as a function of frequency correlated with the function that indicated infinite gain, also as a function of frequency, for the unbiased parametric amplifier [17]. More recently the importance of chaos in intrinsic JJs, and its effects on the IV-characteristics and the Shapiro steps in these systems, were stressed in Refs.…”

Section: Introductionmentioning

confidence: 97%

Structured chaos in a devil's staircase of the Josephson junction

Shukrinov

Botha

Medvedeva

et al. 2014

Chaos

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The phase dynamics of Josephson junctions under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior. These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally the influence of the radiation and Josephson junction parameters on the structured chaos is investigated and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.

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Section: Introductionmentioning

confidence: 97%

Structured chaos in a devil's staircase of the Josephson junction

Shukrinov

Botha

Medvedeva

et al. 2014

Chaos

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“…Moreover, there are certain classes of more realistic models which share specific properties of maps such as being low-dimensional and exhibiting certain periodicities. Indeed, theoretical investigations of chaotic billiards subject to external fields [27], of periodic Lorentz gases [28,29], and of pendulum-like differential equations [30,31,32,33,34,35,36] showed that many properties of deterministic transport in maps carry over to these more complex chaotic dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

Fractality of deterministic diffusion in the nonhyperbolic climbing sine map

Korabel

Klages

2004

Physica D: Nonlinear Phenomena

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The nonlinear climbing sine map is a nonhyperbolic dynamical system exhibiting both normal and anomalous diffusion under variation of a control parameter. We show that on a suitable coarse scale this map generates an oscillating parameterdependent diffusion coefficient, similarly to hyperbolic maps, whose asymptotic functional form can be understood in terms of simple random walk approximations. On finer scales we find fractal hierarchies of normal and anomalous diffusive regions as functions of the control parameter. By using a Green-Kubo formula for diffusion the origin of these different regions is systematically traced back to strong dynamical correlations. Starting from the equations of motion of the map these correlations are formulated in terms of fractal generalized Takagi functions obeying generalized de Rham-type functional recursion relations. We finally analyze the measure of the normal and anomalous diffusive regions in the parameter space showing that in both cases it is positive, and that for normal diffusion it increases by increasing the parameter value.

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“…Each junction is characterized by an order parameter phase difference , a critical current i c , capacitance C, and normal resistance R. The junctions are biased with identical ac current sources i 0 cos t, but no dc source is included. This ac-only driving scenario is commonly adopted to probe essential chaotic behavior in Josephson systems 5,8,[11][12][13][14] and in driven pendulums. 15 The dynamical equations for the two junctions are, in this case,…”

Section: A Coupled Parallel-connected Josephson Junctionsmentioning

confidence: 99%

“…3 That is the question addressed in this paper. Thus, two phenomena which have been studied extensively but separately in connection with Josephson junctions-synchronized oscillations 4 and chaotic dynamics [5][6][7][8][9][10] -appear here in combination.…”

Section: Introductionmentioning

confidence: 99%

Intermittent synchronization of resistively coupled chaotic Josephson junctions

2000

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Numerical simulations have been used to investigate the dynamics of a pair of resistively linked Josephson junctions with ac bias. For suitable choices of parameters, the chaotic states of the two junctions become intermittently synchronized. Intervals of synchronization are interleaved between bursts of desynchronized activity. The distributions of these laminar times and their dependence on the coupling strength are determined. The role of phase winding in the definition of synchronization intervals is considered.

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Chaos and noise rise in Josephson junctions

Cited by 141 publications

References 3 publications

Structured chaos in a devil's staircase of the Josephson junction

Structured chaos in a devil's staircase of the Josephson junction

Fractality of deterministic diffusion in the nonhyperbolic climbing sine map

Intermittent synchronization of resistively coupled chaotic Josephson junctions

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