Synchronization of networked oscillators under nonlinear integral coupling

Alexey Pavlov; Anton V. Proskurnikov; Erik Steur; Nathan van de Wouw

doi:10.1016/j.ifacol.2018.12.091

Synchronization of networked oscillators under nonlinear integral coupling

Alexey Pavlov, Anton V. Proskurnikov, Erik Steur, Nathan van de Wouw

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Abstract

In this paper, we consider synchronization of dynamical systems interconnected via nonlinear integral coupling. Integral coupling allows one to achieve synchronization with lower interaction levels (coupling gains) than with linear coupling. Previous results on this topic were obtained for synchronization of several systems with all-to-all interconnections. In this paper, we relax the requirement of all-to-all interconnections and provide two results on exponential synchronization under nonlinear integral coupling for networks with topologies different from all-to-all interconnections. In particular, we provide a high-gain result for an arbitrary interconnection topology and a non-high-gain method for analysis of synchronization for specific topologies. The results are illustrated by simulations of Hindmarsh-Rose neuron oscillators.

Original language	English
Pages (from-to)	56-61
Journal	IFAC-PapersOnLine
Volume	51
Issue number	33
DOIs	https://doi.org/10.1016/j.ifacol.2018.12.091
Publication status	Published - 2018
Event	CHAOS 2018: 5th IFAC Conference on Analysis and Control of Chaotic Systems - Eindhoven, Netherlands Duration: 30 Oct 2018 → 1 Nov 2018

Keywords

Hindmarsh-Rose oscillators
networked systems
neural dynamics
nonlinear systems
Synchronization

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10.1016/j.ifacol.2018.12.091

1-s2.0-S2405896318336346-mainFinal published version, 801 KB

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title = "Synchronization of networked oscillators under nonlinear integral coupling",

abstract = "In this paper, we consider synchronization of dynamical systems interconnected via nonlinear integral coupling. Integral coupling allows one to achieve synchronization with lower interaction levels (coupling gains) than with linear coupling. Previous results on this topic were obtained for synchronization of several systems with all-to-all interconnections. In this paper, we relax the requirement of all-to-all interconnections and provide two results on exponential synchronization under nonlinear integral coupling for networks with topologies different from all-to-all interconnections. In particular, we provide a high-gain result for an arbitrary interconnection topology and a non-high-gain method for analysis of synchronization for specific topologies. The results are illustrated by simulations of Hindmarsh-Rose neuron oscillators.",

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author = "Alexey Pavlov and Proskurnikov, {Anton V.} and Erik Steur and {de Wouw}, {Nathan van}",

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language = "English",

volume = "51",

pages = "56--61",

journal = "IFAC-PapersOnLine",

issn = "2405-8963",

publisher = "Elsevier",

number = "33",

note = "CHAOS 2018: 5th IFAC Conference on Analysis and Control of Chaotic Systems ; Conference date: 30-10-2018 Through 01-11-2018",

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T1 - Synchronization of networked oscillators under nonlinear integral coupling

AU - Pavlov, Alexey

AU - Proskurnikov, Anton V.

AU - Steur, Erik

AU - de Wouw, Nathan van

PY - 2018

Y1 - 2018

N2 - In this paper, we consider synchronization of dynamical systems interconnected via nonlinear integral coupling. Integral coupling allows one to achieve synchronization with lower interaction levels (coupling gains) than with linear coupling. Previous results on this topic were obtained for synchronization of several systems with all-to-all interconnections. In this paper, we relax the requirement of all-to-all interconnections and provide two results on exponential synchronization under nonlinear integral coupling for networks with topologies different from all-to-all interconnections. In particular, we provide a high-gain result for an arbitrary interconnection topology and a non-high-gain method for analysis of synchronization for specific topologies. The results are illustrated by simulations of Hindmarsh-Rose neuron oscillators.

AB - In this paper, we consider synchronization of dynamical systems interconnected via nonlinear integral coupling. Integral coupling allows one to achieve synchronization with lower interaction levels (coupling gains) than with linear coupling. Previous results on this topic were obtained for synchronization of several systems with all-to-all interconnections. In this paper, we relax the requirement of all-to-all interconnections and provide two results on exponential synchronization under nonlinear integral coupling for networks with topologies different from all-to-all interconnections. In particular, we provide a high-gain result for an arbitrary interconnection topology and a non-high-gain method for analysis of synchronization for specific topologies. The results are illustrated by simulations of Hindmarsh-Rose neuron oscillators.

KW - Hindmarsh-Rose oscillators

KW - networked systems

KW - neural dynamics

KW - nonlinear systems

KW - Synchronization

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DO - 10.1016/j.ifacol.2018.12.091

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Synchronization of networked oscillators under nonlinear integral coupling

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