Universality in three-frequency resonances

被引:25
作者
Cartwright, JHE [1 ]
González, DL
Piro, O
机构
[1] UGR, CSIC, IACT, Inst Andaluz Cienicas de la Tierra, E-18071 Granada, Spain
[2] CNR, Ist Lamel, I-40129 Bologna, Italy
[3] UIB, CSIC, Inst Mediterrani Estudis Avancats, IMEDA, E-07071 Palma de Mallorca, Spain
关键词
D O I
10.1103/PhysRevE.59.2902
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
We investigate the hierarchical structure of three-frequency resonances in nonlinear dynamical systems with three interacting frequencies. We hypothesize an ordering of these resonances based on a generalization of the Farey tree organization from two frequencies to three. In experiments and numerical simulations we demonstrate that our hypothesis describes the hierarchies of three-frequency resonances in representative dynamical systems. We conjecture that this organization may be universal across a large class of three-frequency systems. [S1063-651X(99)14803-7].
引用
收藏
页码:2902 / 2906
页数:5
相关论文
共 14 条
[1]   BIFURCATIONS FROM AN INVARIANT CIRCLE FOR 2-PARAMETER FAMILIES OF MAPS OF THE PLANE - A COMPUTER-ASSISTED STUDY [J].
ARONSON, DG ;
CHORY, MA ;
HALL, GR ;
MCGEHEE, RP .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 83 (03) :303-354
[2]   THE BOGDANOV MAP: BIFURCATIONS, MODE LOCKING, AND CHAOS IN A DISSIPATIVE SYSTEM [J].
Arrowsmith, David K. ;
Cartwright, Julyan H. E. ;
Lansbury, Alexis N. ;
Place, Colin M. .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1993, 3 (04) :803-842
[3]   3 COUPLED OSCILLATORS - MODE-LOCKING, GLOBAL BIFURCATIONS AND TOROIDAL CHAOS [J].
BAESENS, C ;
GUCKENHEIMER, J ;
KIM, S ;
MACKAY, RS .
PHYSICA D, 1991, 49 (03) :387-475
[4]  
CALVO O, IN PRESS IEEE T CIRC
[5]   QUASIPERIODICITY AND CHAOS IN A SYSTEM WITH 3 COMPETING FREQUENCIES [J].
CUMMING, A ;
LINSAY, PS .
PHYSICAL REVIEW LETTERS, 1988, 60 (26) :2719-2722
[6]   SCALING LAWS FOR MODE LOCKINGS IN CIRCLE MAPS [J].
CVITANOVIC, P ;
SHRAIMAN, B ;
SODERBERG, B .
PHYSICA SCRIPTA, 1985, 32 (04) :263-270
[7]   CHAOS IN A NON-LINEAR DRIVEN OSCILLATOR WITH EXACT SOLUTION [J].
GONZALEZ, DL ;
PIRO, O .
PHYSICAL REVIEW LETTERS, 1983, 50 (12) :870-872
[8]   SYMMETRIC KICKED SELF-OSCILLATORS - ITERATED MAPS, STRANGE ATTRACTORS, AND SYMMETRY OF THE PHASE-LOCKING FAREY HIERARCHY [J].
GONZALEZ, DL ;
PIRO, O .
PHYSICAL REVIEW LETTERS, 1985, 55 (01) :17-20
[9]  
Hao B. L., 1989, ELEMENTARY SYMBOLIC
[10]  
Hardy G., 1975, INTRO THEORY NUMBERS, V4