Scaling for small random perturbations of golden critical circle maps

Hamm, Andreas; Graham, R.

doi:10.1103/physreva.46.6323

Cited by 16 publications

(8 citation statements)

References 23 publications

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“…Our work puts the phenomena in complex analytic map into the same context in respect to the effect of noise, as other situations of universal scaling behavior: period doubling [3,4], intermittency [9], quasiperiodicity [10], bicriticality [11], scaling phenomena in Hamiltonian systems [12,13]. So, this specific field is enriched with one more nontrivial example of the scaling behavior linked with presence of noise.…”

Section: Resultsmentioning

confidence: 99%

“…for the onset of chaos via quasiperiodicity and intermittency [5,6], as well as for some situations arising in the multiparameter analysis of transition to chaos [7] or to strange nonchaotic attractors [8]. In particular, the effects of noise on the dynamics have been studied in dissipative systems for intermittency [9], quasiperiodicity [10], bicritical behavior [11], and in Hamiltonian systems for period doubling [12] and KAM-torus destruction [13].…”

Section: Introductionmentioning

confidence: 99%

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Effect of noise on the dynamics of a complex map at the period-tripling accumulation point

2004

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As shown recently [O.B. Isaeva et al., Phys. Rev. E 64, 055201 (2001)], the phenomena intrinsic to dynamics of complex analytic maps under appropriate conditions may occur in physical systems. We study scaling regularities associated with the effect of additive noise upon the period-tripling bifurcation cascade generalizing the renormalization group approach of Crutchfield et al. [Phys. Rev. Lett. 46, 933 (1981)] and Shraiman et al. [Phys. Rev. Lett. 46, 935 (1981)], originally developed for the period doubling transition to chaos in the presence of noise. The universal constant determining the rescaling rule for the intensity of the noise in period tripling is found to be gamma=12.206 640 9 em leader. Numerical evidence of the expected scaling is demonstrated.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of noise on the dynamics of a complex map at the period-tripling accumulation point

2004

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“…We substitute expression for a(t) in the abridged equation (5) and separate the real and imaginary parts.…”

Section: Investigated Systemmentioning

confidence: 99%

“…Thus the known illustrations of scaling, generally speaking, become impossible, because they assume as much as close approach to a critical point. Uncommonly, that the renormalization group method can be generalized on a case of systems with noise (see for example, [2][3][4][5][6][7]). Due to this it is possible to distribute on stochastic systems the scaling property.…”

Section: Introductionmentioning

confidence: 99%

Peculiarities of Scaling in Models of Duffing Oscillator Under Action of Kicks With Random Modulation of Parameters

Кузнецов

Sedova

2008

Fluct. Noise Lett.

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“…The discrete time version [8,9,26] has been used successfully to investigate the influence of noise on renormalisation schemes in the context of transitions from regular to chaotic behaviour [27], and other universal aspects of the influence of noise on bifurcations [28].…”

Section: Proofmentioning

confidence: 99%

Uncertain dynamical systems defined by pseudomeasures

Hamm

1997

Journal of Mathematical Physics

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This paper deals with uncertain dynamical systems in which predictions about the future state of a system are assessed by so called pseudomeasures. Two special cases are stochastic dynamical systems, where the pseudomeasure is the conventional probability measure, and fuzzy dynamical systems in which the pseudomeasure is a so called possibility measure.New results about possibilistic systems and their relation to deterministic and to stochastic systems are derived by using idempotent pseudolinear algebra.By expressing large deviation estimates for stochastic perturbations in terms of possibility measures, we obtain a new interpretation of the Freidlin-Wentzell quasipotentials for stochastic perturbations of dynamical systems as invariant possibility densities.

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Scaling for small random perturbations of golden critical circle maps

Cited by 16 publications

References 23 publications

Effect of noise on the dynamics of a complex map at the period-tripling accumulation point

Effect of noise on the dynamics of a complex map at the period-tripling accumulation point

Peculiarities of Scaling in Models of Duffing Oscillator Under Action of Kicks With Random Modulation of Parameters

Uncertain dynamical systems defined by pseudomeasures

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