Three-frequency resonances in dynamical systems

被引：5

作者：

Calvo, O ^{[1
]}

Cartwright, JHE

González, DL

Piro, O

Rosso, OA

机构：

[1] Natl Univ La Plata, Fac Ingn, Dept Electrotecn, LEICI,CICPBA, RA-1900 La Plata, Argentina

[2] Univ Granada, CSIC, IACT, E-18071 Granada, Spain

[3] CNR, Ist Lamel, I-40129 Bologna, Italy

[4] Univ Illes Balears, CSIC, IMEDEA, Inst Mediterrani Estudis Avancats, E-07071 Palma de Mallorca, Spain

[5] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Inst Calculo, RA-1428 Buenos Aires, DF, Argentina

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 1999年 / 9卷 / 11期

关键词：

D O I：

10.1142/S0218127499001607

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate numerically and experimentally dynamical systems having three interacting frequencies: a discrete mapping (a circle map), an exactly solvable model (a system of coupled ordinary differential equations), and an experimental device (an electronic oscillator). We compare the hierarchies of three-frequency resonances we find in each of these systems. All three show similar qualitative behaviour, suggesting the existence of generic features in the parameter-space organization of three-frequency resonances.

引用

页码：2181 / 2187

页数：7

共 13 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]

Arrowsmith D.K., 1990, INTRO DYNAMICAL SYST

[3] 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

[4] 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

[5]

CALVO O, 1999, IN PRESS IEEE T CIRC

[6] Nonlinear dynamics of the perceived pitch of complex sounds [J].

Cartwright, JHE ;

González, DL ;

Piro, O .

PHYSICAL REVIEW LETTERS, 1999, 82 (26) :5389-5392

[7] Universality in three-frequency resonances [J].

Cartwright, JHE ;

González, DL ;

Piro, O .

PHYSICAL REVIEW E, 1999, 59 (03) :2902-2906

[8] SCALING LAWS FOR MODE LOCKINGS IN CIRCLE MAPS [J].

CVITANOVIC, P ;

SHRAIMAN, B ;

SODERBERG, B .

PHYSICA SCRIPTA, 1985, 32 (04) :263-270

[9] CHAOS IN A NON-LINEAR DRIVEN OSCILLATOR WITH EXACT SOLUTION [J].

GONZALEZ, DL ;

PIRO, O .

PHYSICAL REVIEW LETTERS, 1983, 50 (12) :870-872

[10] 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

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