State-dependent effective interactions in oscillator networks through coupling functions with dead zones

Peter Ashwin; Christian Bick; Camille Poignard

doi:10.1098/rsta.2019.0042

State-dependent effective interactions in oscillator networks through coupling functions with dead zones

Peter Ashwin^*, Christian Bick, Camille Poignard

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

The dynamics of networks of interacting dynamical systems depend on the nature of the coupling between individual units. We explore networks of oscillatory units with coupling functions that have 'dead zones', that is the coupling functions are zero on sets with interior. For such networks, it is convenient to look at the effective interactions between units rather than the (fixed) structural connectivity to understand the network dynamics. For example, oscillators may effectively decouple in particular phase configurations. Along trajectories, the effective interactions are not necessarily static, but the effective coupling may evolve in time. Here, we formalize the concepts of dead zones and effective interactions. We elucidate how the coupling function shapes the possible effective interaction schemes and how they evolve in time. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Original language	English
Article number	20190042
Journal	Philosophical Transactions of the Royal Society. Series A, Mathematical, Physical and Engineering Sciences
Volume	377
Issue number	2160
DOIs	https://doi.org/10.1098/rsta.2019.0042
Publication status	Published - 16 Dec 2019
Externally published	Yes

Funding

Data accessibility. This article has no additional data. Authors’ contributions. All authors contributed to the design of the research and the writing of the manuscript. Competing interests. We declare we have no competing interests. Funding. P.A. and C.P. were funded by EPSRC Centre for Predictive Modelling in Healthcare, grant no. EP/N014391/1. Acknowledgements. The authors thank B. Fernandez, Yu. Maistrenko and T. Pereira for useful discussions, and the referees for some very useful comments.

Funders	Funder number
P.A.
Engineering and Physical Sciences Research Council	EP/N014391/1
EPSRC Centre for Doctoral Training in Medical Imaging

Keywords

Coupled oscillator
Coupling function
Network dynamical system

Access to Document

10.1098/rsta.2019.0042

Persistent URL (handle)

Persistent link

Cite this

@article{9ccdc1ff0bc448f59e7be01e43741f98,

title = "State-dependent effective interactions in oscillator networks through coupling functions with dead zones",

abstract = "The dynamics of networks of interacting dynamical systems depend on the nature of the coupling between individual units. We explore networks of oscillatory units with coupling functions that have 'dead zones', that is the coupling functions are zero on sets with interior. For such networks, it is convenient to look at the effective interactions between units rather than the (fixed) structural connectivity to understand the network dynamics. For example, oscillators may effectively decouple in particular phase configurations. Along trajectories, the effective interactions are not necessarily static, but the effective coupling may evolve in time. Here, we formalize the concepts of dead zones and effective interactions. We elucidate how the coupling function shapes the possible effective interaction schemes and how they evolve in time. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.",

keywords = "Coupled oscillator, Coupling function, Network dynamical system",

author = "Peter Ashwin and Christian Bick and Camille Poignard",

year = "2019",

month = dec,

day = "16",

doi = "10.1098/rsta.2019.0042",

language = "English",

volume = "377",

journal = "Philosophical Transactions of the Royal Society. Series A, Mathematical, Physical and Engineering Sciences",

issn = "1364-503X",

publisher = "The Royal Society",

number = "2160",

}

State-dependent effective interactions in oscillator networks through coupling functions with dead zones. / Ashwin, Peter; Bick, Christian; Poignard, Camille.
In: Philosophical Transactions of the Royal Society. Series A, Mathematical, Physical and Engineering Sciences, Vol. 377, No. 2160, 20190042, 16.12.2019.

Research output: Contribution to Journal › Article › Academic › peer-review

TY - JOUR

T1 - State-dependent effective interactions in oscillator networks through coupling functions with dead zones

AU - Ashwin, Peter

AU - Bick, Christian

AU - Poignard, Camille

PY - 2019/12/16

Y1 - 2019/12/16

N2 - The dynamics of networks of interacting dynamical systems depend on the nature of the coupling between individual units. We explore networks of oscillatory units with coupling functions that have 'dead zones', that is the coupling functions are zero on sets with interior. For such networks, it is convenient to look at the effective interactions between units rather than the (fixed) structural connectivity to understand the network dynamics. For example, oscillators may effectively decouple in particular phase configurations. Along trajectories, the effective interactions are not necessarily static, but the effective coupling may evolve in time. Here, we formalize the concepts of dead zones and effective interactions. We elucidate how the coupling function shapes the possible effective interaction schemes and how they evolve in time. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

AB - The dynamics of networks of interacting dynamical systems depend on the nature of the coupling between individual units. We explore networks of oscillatory units with coupling functions that have 'dead zones', that is the coupling functions are zero on sets with interior. For such networks, it is convenient to look at the effective interactions between units rather than the (fixed) structural connectivity to understand the network dynamics. For example, oscillators may effectively decouple in particular phase configurations. Along trajectories, the effective interactions are not necessarily static, but the effective coupling may evolve in time. Here, we formalize the concepts of dead zones and effective interactions. We elucidate how the coupling function shapes the possible effective interaction schemes and how they evolve in time. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

KW - Coupled oscillator

KW - Coupling function

KW - Network dynamical system

UR - http://www.scopus.com/inward/record.url?scp=85074177721&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074177721&partnerID=8YFLogxK

U2 - 10.1098/rsta.2019.0042

DO - 10.1098/rsta.2019.0042

M3 - Article

C2 - 31656136

AN - SCOPUS:85074177721

SN - 1364-503X

VL - 377

JO - Philosophical Transactions of the Royal Society. Series A, Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society. Series A, Mathematical, Physical and Engineering Sciences

IS - 2160

M1 - 20190042

ER -

State-dependent effective interactions in oscillator networks through coupling functions with dead zones

Abstract

Funding

Keywords

Access to Document

Persistent URL (handle)

Other files and links

Fingerprint

Cite this