ABOUT SCALING PROPERTIES IN THE NOISY CIRCLE MAP AT THE GOLDEN-MEAN WINDING NUMBER
Cite this article as:
Kuznetsov A. P., Kuznetsov S. P., Sedova Y. V. ABOUT SCALING PROPERTIES IN THE NOISY CIRCLE MAP AT THE GOLDEN-MEAN WINDING NUMBER. Izvestiya VUZ. Applied Nonlinear Dynamics, 2005, vol. 13, iss. 6, pp. 56-76. DOI: https://doi.org/10.18500/0869-6632-2005-13-5-56-76
Scaling regularities are examined associated with effect of additive noise upon a critical circle map at the golden-mean winding number. On a basis of the RG approach of Hamm and Graham [1] we present an improved numerical estimate for the scaling constant responsible for the effect of noise, g = 2:3061852653::: Decrease of the noise amplitude by this number ensures possibility of observation for one more level of fractal-like structure associated with increase of characteristic time scale by factor (p5 + 1)=2. Numeric results demonstrating evidence of the expected scaling are presented, e.g. portraits of the noisy attractors, devil’s staircase plots, and Lyapunov charts.
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BibTeX
author = {A. P. Kuznetsov and Sergey P. Kuznetsov and Yu. V. Sedova },
title = {ABOUT SCALING PROPERTIES IN THE NOISY CIRCLE MAP AT THE GOLDEN-MEAN WINDING NUMBER},
year = {2005},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {13},number = {6},
url = {https://old-andjournal.sgu.ru/en/articles/about-scaling-properties-in-the-noisy-circle-map-at-the-golden-mean-winding-number},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2005-13-5-56-76},pages = {56--76},issn = {0869-6632},
keywords = {-},
abstract = {Scaling regularities are examined associated with effect of additive noise upon a critical circle map at the golden-mean winding number. On a basis of the RG approach of Hamm and Graham [1] we present an improved numerical estimate for the scaling constant responsible for the effect of noise, g = 2:3061852653::: Decrease of the noise amplitude by this number ensures possibility of observation for one more level of fractal-like structure associated with increase of characteristic time scale by factor (p5 + 1)=2. Numeric results demonstrating evidence of the expected scaling are presented, e.g. portraits of the noisy attractors, devil’s staircase plots, and Lyapunov charts. }}