Coupled Mobius maps as a tool to model Kuramoto phase synchronization

被引：8

作者：

Gong, Chen Chris ^{[1
]}

Toenjes, Ralf ^{[1
]}

Pikovsky, Arkady ^{[1
,2
]}

机构：

[1] Univ Potsdam, Inst Phys & Astron, Karl Liebknecht Str 32, D-14476 Potsdam, Germany

[2] Nizhnii Novgorod State Univ, Dept Control Theory, Gagarin Ave 23, Nizhnii Novgorod 606950, Russia

来源：

PHYSICAL REVIEW E | 2020年 / 102卷 / 02期

基金：

俄罗斯科学基金会; 巴西圣保罗研究基金会;

关键词：

TRANSITIONS; ENSEMBLES; BEHAVIOR;

D O I：

10.1103/PhysRevE.102.022206

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 propose Mobius maps as a tool to model synchronization phenomena in coupled phase oscillators. Not only does the map provide fast computation of phase synchronization, it also reflects the underlying group structure of the sinusoidally coupled continuous phase dynamics. We study map versions of various known continuous-time collective dynamics, such as the synchronization transition in the Kuramoto-Sakaguchi model of nonidentical oscillators, chimeras in two coupled populations of identical phase oscillators, and Kuramoto-Battogtokh chimeras on a ring, and demonstrate similarities and differences between the iterated map models and their known continuous-time counterparts.

引用

页数：12

共 50 条

[1] Solvable model for chimera states of coupled oscillators [J].

Abrams, Daniel M. ;

Mirollo, Rennie ;

Strogatz, Steven H. ;

Wiley, Daniel A. .

PHYSICAL REVIEW LETTERS, 2008, 101 (08)

[2] Chimera states for coupled oscillators [J].

Abrams, DM ;

Strogatz, SH .

PHYSICAL REVIEW LETTERS, 2004, 93 (17) :174102-1

[3] A STUDY OF LOCKING PHENOMENA IN OSCILLATORS [J].

ADLER, R .

PROCEEDINGS OF THE INSTITUTE OF RADIO ENGINEERS, 1946, 34 (06) :351-357

[4]

[Anonymous], 1997, Encyclopedia of Mathematics and its Applications

[5]

Bauer M., 2009, NETWORK-COMP NEURAL, V2, P345

[6] Generative models of cortical oscillations: neurobiological implications of the Kuramoto model [J].

Breakspear, Michael ;

Heitmann, Stewart ;

Daffertshofer, Andreas .

FRONTIERS IN HUMAN NEUROSCIENCE, 2010, 4

[7] Rotation number quantization effect [J].

Buchstaber, V. M. ;

Karpov, O. V. ;

Tertychniy, S. I. .

THEORETICAL AND MATHEMATICAL PHYSICS, 2010, 162 (02) :211-221

[8] Role of local network oscillations in resting-state functional connectivity [J].

Cabral, Joana ;

Hugues, Etienne ;

Sporns, Olaf ;

Deco, Gustavo .

NEUROIMAGE, 2011, 57 (01) :130-139

[9]

Chakraborty S, 2014, 2014 INTERNATIONAL CONFERENCE ON SIGNAL PROPAGATION AND COMPUTER TECHNOLOGY (ICSPCT 2014), P368, DOI 10.1109/ICSPCT.2014.6884959

[10] Synchronization in coupled sine circle maps [J].

Chatterjee, N ;

Gupte, N .

PHYSICAL REVIEW E, 1996, 53 (05) :4457-4466

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