Synchronization bound for networks of nonlinear oscillators

Elizabeth N. Davison; Biswadip Dey; Naomi Ehrich Leonard

doi:10.1109/ALLERTON.2016.7852359

Synchronization bound for networks of nonlinear oscillators

Elizabeth N. Davison, Biswadip Dey, Naomi Ehrich Leonard

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

8 Scopus citations

Abstract

Investigation of synchronization phenomena in networks of coupled nonlinear oscillators plays a pivotal role in understanding the behavior of biological and mechanical systems with oscillatory properties. We derive a general sufficient condition for synchronization of a network of nonlinear oscillators using a nonsmooth Lyapunov function, and we obtain conditions under which synchronization is guaranteed for a network of Fitzhugh-Nagumo (FN) oscillators in biologically relevant model parameter regimes. We incorporate two types of heterogeneity into our study of FN oscillators: 1) the network structure is arbitrary and 2) the oscillators have non-identical external inputs. Understanding the effects of heterogeneities on synchronization of oscillators with inputs provides a promising step toward control of key aspects of networked oscillatory systems.

Original language	English (US)
Title of host publication	54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1110-1115
Number of pages	6
ISBN (Electronic)	9781509045495
DOIs	https://doi.org/10.1109/ALLERTON.2016.7852359
State	Published - Feb 10 2017
Event	54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 - Monticello, United States Duration: Sep 27 2016 → Sep 30 2016

Publication series

Name	54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016

Other

Other	54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
Country/Territory	United States
City	Monticello
Period	9/27/16 → 9/30/16

All Science Journal Classification (ASJC) codes

Artificial Intelligence
Computational Theory and Mathematics
Computer Networks and Communications
Hardware and Architecture
Control and Optimization

Keywords

Complex Networked Systems
Lyapunov Analysis
Nonlinear Oscillators
Synchronization

Access to Document

10.1109/ALLERTON.2016.7852359

Cite this

Davison, E. N., Dey, B., & Leonard, N. E. (2017). Synchronization bound for networks of nonlinear oscillators. In 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 (pp. 1110-1115). Article 7852359 (54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ALLERTON.2016.7852359

Davison, Elizabeth N. ; Dey, Biswadip ; Leonard, Naomi Ehrich. / Synchronization bound for networks of nonlinear oscillators. 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 1110-1115 (54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016).

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abstract = "Investigation of synchronization phenomena in networks of coupled nonlinear oscillators plays a pivotal role in understanding the behavior of biological and mechanical systems with oscillatory properties. We derive a general sufficient condition for synchronization of a network of nonlinear oscillators using a nonsmooth Lyapunov function, and we obtain conditions under which synchronization is guaranteed for a network of Fitzhugh-Nagumo (FN) oscillators in biologically relevant model parameter regimes. We incorporate two types of heterogeneity into our study of FN oscillators: 1) the network structure is arbitrary and 2) the oscillators have non-identical external inputs. Understanding the effects of heterogeneities on synchronization of oscillators with inputs provides a promising step toward control of key aspects of networked oscillatory systems.",

keywords = "Complex Networked Systems, Lyapunov Analysis, Nonlinear Oscillators, Synchronization",

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Davison, EN, Dey, B & Leonard, NE 2017, Synchronization bound for networks of nonlinear oscillators. in 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016., 7852359, 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016, Institute of Electrical and Electronics Engineers Inc., pp. 1110-1115, 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016, Monticello, United States, 9/27/16. https://doi.org/10.1109/ALLERTON.2016.7852359

Synchronization bound for networks of nonlinear oscillators. / Davison, Elizabeth N.; Dey, Biswadip; Leonard, Naomi Ehrich.
54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016. Institute of Electrical and Electronics Engineers Inc., 2017. p. 1110-1115 7852359 (54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - Investigation of synchronization phenomena in networks of coupled nonlinear oscillators plays a pivotal role in understanding the behavior of biological and mechanical systems with oscillatory properties. We derive a general sufficient condition for synchronization of a network of nonlinear oscillators using a nonsmooth Lyapunov function, and we obtain conditions under which synchronization is guaranteed for a network of Fitzhugh-Nagumo (FN) oscillators in biologically relevant model parameter regimes. We incorporate two types of heterogeneity into our study of FN oscillators: 1) the network structure is arbitrary and 2) the oscillators have non-identical external inputs. Understanding the effects of heterogeneities on synchronization of oscillators with inputs provides a promising step toward control of key aspects of networked oscillatory systems.

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Davison EN, Dey B, Leonard NE. Synchronization bound for networks of nonlinear oscillators. In 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016. Institute of Electrical and Electronics Engineers Inc. 2017. p. 1110-1115. 7852359. (54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016). doi: 10.1109/ALLERTON.2016.7852359

Synchronization bound for networks of nonlinear oscillators

Abstract

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