Different types of scaling in the dynamics of period–doubling maps under external periodic driving

Discrete Dynamics in Nature and Society

N. Yu. Ivank’ov¹  S. P. Kuznetsov² 

[1] College of Applied Sciences, Saratov State University, Astrakhanskaja 83, Saratov 410026, Russia;lnstitute of Radio-Engineering and Electronics RAS, Saratov Division, Zelenaya 38, Saratov 410019, Russia;

关键词: Logistic map;    Periodic driving;    Universality;    Scaling.;   

DOI  :  10.1155/S1026022600000546

来源: DOAJ

【 摘 要 】

Based on the renormalization group approach developed by Kuznetsov and Pikovsky (Phys. Lett., A140, 1989, 166) several types of scaling are discussed, which can be observed in a neighborhood of Feigenbaum’s critical point at small amplitudes of the driving. The type of scaling behavior depends on a structure of binary representation of the frequency parameter: F-scaling (Feigenbaum’s) for finite binary fractions, P- and Q-scaling (periodic and quasiperiodic) for periodic binary fractions, andS-scaling (statistical) for non-periodic binary fractions. All types of scaling are illustrated by parameter-plane diagrams for the rescaled Lyapunov exponent.

【 授权许可】

Unknown