Entrainment and Synchronization in Heterogeneous Networks of Haken-Kelso-Bunz (HKB) Oscillators

Francesco Alderisio; Benoit G. Bardy; Mario di Bernardo

Entrainment and Synchronization in Heterogeneous Networks of Haken-Kelso-Bunz (HKB) Oscillators

Francesco Alderisio, Benoit G. Bardy, Mario di Bernardo

Research output: Working paper › Working paper and Preprints

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Abstract

In this paper we consider a heterogeneous network of Haken-Kelso-Bunz (HKB) nonlinear oscillators coupled through both linear and nonlinear interaction protocols. While some work exists on a system made up of only two nonlinearly coupled HKB oscillators as a model of human dynamics during interpersonal coordination tasks, the problem of considering a network of three or more HKBs has not been fully investigated. The aim of our work is to study convergence and synchronization in networks of HKB oscillators as a paradigm of coordination in multiplayer games. Convergence results are obtained under the assumption that the network is connected, simple and undirected. Analytical results are obtained to prove convergence when the oscillators are coupled diffusively. All theoretical results are illustrated via numerical examples. Finally, the effects of adding an external entrainment signal to all the agents in the network are analyzed and a model to account for them is proposed.

Original language	English
Place of Publication	arXiv:1509.00753
Publisher	arXiv.org
Number of pages	34
Volume	1509
Publication status	Published - 2 Sep 2015

Keywords

math.DS
nlin.AO

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http://arxiv.org/abs/1509.00753

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title = "Entrainment and Synchronization in Heterogeneous Networks of Haken-Kelso-Bunz (HKB) Oscillators",

abstract = "In this paper we consider a heterogeneous network of Haken-Kelso-Bunz (HKB) nonlinear oscillators coupled through both linear and nonlinear interaction protocols. While some work exists on a system made up of only two nonlinearly coupled HKB oscillators as a model of human dynamics during interpersonal coordination tasks, the problem of considering a network of three or more HKBs has not been fully investigated. The aim of our work is to study convergence and synchronization in networks of HKB oscillators as a paradigm of coordination in multiplayer games. Convergence results are obtained under the assumption that the network is connected, simple and undirected. Analytical results are obtained to prove convergence when the oscillators are coupled diffusively. All theoretical results are illustrated via numerical examples. Finally, the effects of adding an external entrainment signal to all the agents in the network are analyzed and a model to account for them is proposed.",

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T1 - Entrainment and Synchronization in Heterogeneous Networks of Haken-Kelso-Bunz (HKB) Oscillators

AU - Alderisio, Francesco

AU - Bardy, Benoit G.

AU - Bernardo, Mario di

PY - 2015/9/2

Y1 - 2015/9/2

N2 - In this paper we consider a heterogeneous network of Haken-Kelso-Bunz (HKB) nonlinear oscillators coupled through both linear and nonlinear interaction protocols. While some work exists on a system made up of only two nonlinearly coupled HKB oscillators as a model of human dynamics during interpersonal coordination tasks, the problem of considering a network of three or more HKBs has not been fully investigated. The aim of our work is to study convergence and synchronization in networks of HKB oscillators as a paradigm of coordination in multiplayer games. Convergence results are obtained under the assumption that the network is connected, simple and undirected. Analytical results are obtained to prove convergence when the oscillators are coupled diffusively. All theoretical results are illustrated via numerical examples. Finally, the effects of adding an external entrainment signal to all the agents in the network are analyzed and a model to account for them is proposed.

AB - In this paper we consider a heterogeneous network of Haken-Kelso-Bunz (HKB) nonlinear oscillators coupled through both linear and nonlinear interaction protocols. While some work exists on a system made up of only two nonlinearly coupled HKB oscillators as a model of human dynamics during interpersonal coordination tasks, the problem of considering a network of three or more HKBs has not been fully investigated. The aim of our work is to study convergence and synchronization in networks of HKB oscillators as a paradigm of coordination in multiplayer games. Convergence results are obtained under the assumption that the network is connected, simple and undirected. Analytical results are obtained to prove convergence when the oscillators are coupled diffusively. All theoretical results are illustrated via numerical examples. Finally, the effects of adding an external entrainment signal to all the agents in the network are analyzed and a model to account for them is proposed.

KW - math.DS

KW - nlin.AO

M3 - Working paper and Preprints

VL - 1509

BT - Entrainment and Synchronization in Heterogeneous Networks of Haken-Kelso-Bunz (HKB) Oscillators

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