Synchronization of two non-scalar-coupled limit-cycle oscillators

被引:38
作者
Ivanchenko, MV
Osipov, GV
Shalfeev, VD
Kurths, J
机构
[1] Nizhny Novgorod Univ, Dept Radiophys, Nizhnii Novgorod 603600, Russia
[2] Univ Potsdam, Inst Phys, D-14415 Potsdam, Germany
基金
俄罗斯基础研究基金会;
关键词
synchronization; coupled oscillators; bifurcations;
D O I
10.1016/j.physd.2003.09.035
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Being one of the fundamental phenomena in nonlinear science, synchronization of oscillations has permanently remained an object of intensive research. Development of many asymptotic methods and numerical simulations has allowed an understanding and explanation of various phenomena of self-synchronization. But even in the classical case of coupled van der Pol oscillators a full description of all possible dynamical regimes, their mutual transitions and characteristics is still lacking. We present here a study of the phenomenon of mutual synchronization for two non-scalar-coupled non-identical limit-cycle oscillators and analyze phase, frequency and amplitude characteristics of synchronization regimes. A series of bifurcation diagrams that we obtain exhibit various regions of qualitatively different behavior. Among them we find mono-, bi- and multistability regions, beating and "oscillation death" ones; also a region, where one of the oscillators dominates the other one is observed. The frequency characteristics that we obtain reveal three qualitatively different types of synchronization: (i) on the mean frequency (the in-phase synchronization), (ii) with a shift from the mean frequency caused by a conservative coupling term (the anti-phase synchronization), and (iii) on the frequency of one of the oscillators (when one oscillator dominates the other). (C) 2003 Elsevier B.V. All rights reserved.
引用
收藏
页码:8 / 30
页数:23
相关论文
共 23 条
[1]  
Andronov A., 1930, ZH PRIKL FIZ J APPL, V7, P3
[2]  
Andronov A. A., 1930, ARCH ELEKTROTECH, VXXIV, P99, DOI 10.1007/BF01659580
[3]  
[Anonymous], P CAMBRIDGE PHIL SOC
[4]   The synchronization of chaotic systems [J].
Boccaletti, S ;
Kurths, J ;
Osipov, G ;
Valladares, DL ;
Zhou, CS .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2002, 366 (1-2) :1-101
[5]  
BREMSEN AS, 1941, Z TECHNICHESKOI FIZI, V11, P959
[6]  
CARTWRIGHT ML, 1945, J LOND MATH SOC, V20, DOI DOI 10.1112/JLMS/S1-20.3.180
[7]  
CARTWRIGHT ML, 1948, J I ELECT ENG LOND, V95, P88
[8]  
CHACRABORTY T, 1988, INT J NONLINEAR MECH, V23, P369
[9]   OSCILLATOR DEATH IN POPULATIONS OF ALL TO ALL COUPLED NONLINEAR OSCILLATORS [J].
ERMENTROUT, GB .
PHYSICA D, 1990, 41 (02) :219-231
[10]  
GAPONOV VI, 1936, ZH TEKH FIZ, V6, P5