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

Shukrinov, Yu. M.; Botha, A. E.; Medvedeva, S. Yu.; Kolahchi, M. R.; Irie, Atsushi

doi:10.1063/1.4890573

Cited by 33 publications

(16 citation statements)

References 68 publications

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“…Contrary to our case, chaos has been observed in the spatiotemporal dynamics of moving kinks in the damped dc driven FK model where the resonances appear due to competitions between the moving kinks and their radiated phase modes [26]. Also, structured chaos has been observed in a Josephson junction systems where chaotic regions appear between the subharmonic Shapiro steps at certain values of system parameters [27].…”

Section: Resultscontrasting

confidence: 82%

Farey sequence in the appearance of subharmonic Shapiro steps

2015

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The largest Lyapunov exponent has been examined in the dynamical-mode locking phenomena of the ac+dc driven dissipative Frenkel-Kontorova model with deformable substrate potential. Due to deformation, large fractional and higher order subharmonic steps appear in the response function of the system. Computation of the largest Lyapunov exponent as a way to verify their presence led to the observation of the Farey sequence. In the standard regime, the appearance of half-integer and other subharmonic steps between the large harmonic steps, and their relative sizes follow the Farey construction. In the nonstandard regime, however, the half-integer steps are larger than harmonic ones, and Farey construction is only present in the appearance of higher order subharmonic steps. The examination of Lyapunov exponents has also shown that regardless of the substrate potential or deformation, there was no chaos in the system.

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Section: Resultscontrasting

confidence: 82%

Farey sequence in the appearance of subharmonic Shapiro steps

2015

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“…These results in Fig Though the LE analysis is applied here to investigate the properties of Shapiro steps it also gives us a possibility to investigate weather the model exibits chaotic behavior. Presence of chaos has been studied in the Josephson junction systems where even on-step positive Lyapunov exponent was found [13,32]. It is interesting that in our studies of the overdamped dc+ac driven FK model, even in the case of incommensurate structures and the large values of ac amplitude F ac , chaos has never been detected.…”

Section: Dc+ac Driven Systemmentioning

confidence: 81%

Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces

Odavić

Mali

Tekić

et al. 2017

Communications in Nonlinear Science and Numerical Simulation

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Dynamics of driven dissipative Frenkel-Kontorova model is examined by using largest Lyapunov exponent computational technique. Obtained results show that besides the usual way where behavior of the system in the presence of external forces is studied by analyzing its dynamical response function, the largest Lyapunov exponent analysis can represent a very convenient tool to examine system dynamics. In the dc driven systems, the critical depinning force for particular structure could be estimated by computing the largest Lyapunov exponent. In the dc+ac driven systems, if the substrate potential is the standard sinusoidal one, calculation of the largest Lyapunov exponent offers a more sensitive way to detect the presence of Shapiro steps. When the amplitude of the ac force is varied the behavior of the largest Lyapunov exponent in the pinned regime completely reflects the behavior of Shapiro steps and the critical depinning force, in particular, it represents the mirror image of the amplitude dependence of critical depinning force. This points out an advantage of this technique since by calculating the largest Lyapunov exponent in the pinned regime we can get an insight into the dynamics of the system when driving forces are applied.

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“…A spontaneous symmetry-breaking bifurcation 16 (SSB) is additionally shown. Chaos-chaos transitions involving phase space explosions, like the one occurring at ρ p between partially predictable and strong chaos (which is in part intermittent 17 ), have been studied previously in the context of quadratic maps 18 and driven Josephson junctions 10 , 11 . They are due to the collision of an unstable manifold with the attracting chaotic set, an interior crisis 18 which is a typical example of a global bifurcation 6 .…”

Section: Resultsmentioning

confidence: 99%

“…Our observation of partial predictability may hence be especially of relevance for natural systems having a tendency to self-organize close to criticality 9 , as it implies that the system will hover continuously close to the transition between laminar and chaotic flow 6 . Another example of PPC is the case of phase locked chaos observed in driven Josephson junctions 10 , 11 .…”

Section: Introductionmentioning

confidence: 99%

How to test for partially predictable chaos

Wernecke¹,

Sándor²,

Gros³

2017

Sci Rep

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For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation can split into an initial exponential decrease and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. Both processes can be either of the same or of very different time scales. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and remain partially predictable. Standard tests for chaos widely use inter-orbital correlations as an indicator. However, testing partially predictable chaos yields mostly ambiguous results, as this type of chaos is characterized by attractors of fractally broadened braids. For a resolution we introduce a novel 0–1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories. This test robustly discriminates chaos, including partially predictable chaos, from laminar flow. Additionally using the finite time cross-correlation of pairs of initially close trajectories, we are able to identify laminar flow as well as strong and partially predictable chaos in a 0–1 manner solely from the properties of pairs of trajectories.

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

Cited by 33 publications

References 68 publications

Farey sequence in the appearance of subharmonic Shapiro steps

Farey sequence in the appearance of subharmonic Shapiro steps

Application of largest Lyapunov exponent analysis on the studies of dynamics under external forces

How to test for partially predictable chaos

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