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Kuznecov A. P., Kuznecov S. P., Sedova J. 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:


About scaling properties in the noisy circle map at the golden-mean winding number

Kuznecov Aleksandr Petrovich, Saratov State University
Kuznecov Sergej Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Sedova Julija Viktorovna, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

Scaling regularities are examined associated with e?ect 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 e?ect 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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