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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: 10.18500/0869-6632-2005-13-5-56-76

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

Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Sedova Yu. V., Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

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, γ = 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 ( √ 5 + 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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