Stochastic phase-cohesiveness of discrete-time kuramoto oscillators in a frequency-dependent tree network

Matin Jafarian; Mohammad H. Mamduhi; Karl H. Johansson

doi:10.23919/ECC.2019.8796107

Stochastic phase-cohesiveness of discrete-time kuramoto oscillators in a frequency-dependent tree network

Matin Jafarian, Mohammad H. Mamduhi, Karl H. Johansson

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

Abstract

This paper presents the notion of stochastic phase-cohesiveness based on the concept of recurrent Markov chains and studies the conditions under which a discrete-time stochastic Kuramoto model is phase-cohesive. It is assumed that the exogenous frequencies of the oscillators are combined with random variables representing uncertainties. A bidirectional tree network is considered such that each oscillator is coupled to its neighbors with a coupling law which depends on its own noisy exogenous frequency. In addition, an undirected tree network is studied. For both cases, a sufficient condition for the common coupling strength ( kappa) and a necessary condition for the sampling-period are derived such that the stochastic phase-cohesiveness is achieved. The analysis is performed within the stochastic systems framework and validated by means of numerical simulations.

Original language	English
Title of host publication	2019 18th European Control Conference, ECC 2019
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	1987-1992
Number of pages	6
ISBN (Electronic)	9783907144008
DOIs	https://doi.org/10.23919/ECC.2019.8796107
Publication status	Published - Jun 2019
Externally published	Yes
Event	18th European Control Conference, ECC 2019 - Naples, Italy Duration: 25 Jun 2019 → 28 Jun 2019

Publication series

Name	2019 18th European Control Conference, ECC 2019

Conference

Conference	18th European Control Conference, ECC 2019
Country/Territory	Italy
City	Naples
Period	25/06/19 → 28/06/19

Bibliographical note

Publisher Copyright:
© 2019 EUCA.

ASJC Scopus subject areas

Instrumentation
Control and Optimization

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10.23919/ECC.2019.8796107

Cite this

Jafarian, M., Mamduhi, M. H., & Johansson, K. H. (2019). Stochastic phase-cohesiveness of discrete-time kuramoto oscillators in a frequency-dependent tree network. In 2019 18th European Control Conference, ECC 2019 (pp. 1987-1992). Article 8796107 (2019 18th European Control Conference, ECC 2019). Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.23919/ECC.2019.8796107

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title = "Stochastic phase-cohesiveness of discrete-time kuramoto oscillators in a frequency-dependent tree network",

abstract = "This paper presents the notion of stochastic phase-cohesiveness based on the concept of recurrent Markov chains and studies the conditions under which a discrete-time stochastic Kuramoto model is phase-cohesive. It is assumed that the exogenous frequencies of the oscillators are combined with random variables representing uncertainties. A bidirectional tree network is considered such that each oscillator is coupled to its neighbors with a coupling law which depends on its own noisy exogenous frequency. In addition, an undirected tree network is studied. For both cases, a sufficient condition for the common coupling strength ( kappa) and a necessary condition for the sampling-period are derived such that the stochastic phase-cohesiveness is achieved. The analysis is performed within the stochastic systems framework and validated by means of numerical simulations.",

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note = "Publisher Copyright: {\textcopyright} 2019 EUCA.; 18th European Control Conference, ECC 2019 ; Conference date: 25-06-2019 Through 28-06-2019",

year = "2019",

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doi = "10.23919/ECC.2019.8796107",

language = "English",

series = "2019 18th European Control Conference, ECC 2019",

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Jafarian, M, Mamduhi, MH & Johansson, KH 2019, Stochastic phase-cohesiveness of discrete-time kuramoto oscillators in a frequency-dependent tree network. in 2019 18th European Control Conference, ECC 2019., 8796107, 2019 18th European Control Conference, ECC 2019, Institute of Electrical and Electronics Engineers (IEEE), pp. 1987-1992, 18th European Control Conference, ECC 2019, Naples, Italy, 25/06/19. https://doi.org/10.23919/ECC.2019.8796107

Stochastic phase-cohesiveness of discrete-time kuramoto oscillators in a frequency-dependent tree network. / Jafarian, Matin; Mamduhi, Mohammad H.; Johansson, Karl H.
2019 18th European Control Conference, ECC 2019. Institute of Electrical and Electronics Engineers (IEEE), 2019. p. 1987-1992 8796107 (2019 18th European Control Conference, ECC 2019).

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

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AB - This paper presents the notion of stochastic phase-cohesiveness based on the concept of recurrent Markov chains and studies the conditions under which a discrete-time stochastic Kuramoto model is phase-cohesive. It is assumed that the exogenous frequencies of the oscillators are combined with random variables representing uncertainties. A bidirectional tree network is considered such that each oscillator is coupled to its neighbors with a coupling law which depends on its own noisy exogenous frequency. In addition, an undirected tree network is studied. For both cases, a sufficient condition for the common coupling strength ( kappa) and a necessary condition for the sampling-period are derived such that the stochastic phase-cohesiveness is achieved. The analysis is performed within the stochastic systems framework and validated by means of numerical simulations.

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ER -

Stochastic phase-cohesiveness of discrete-time kuramoto oscillators in a frequency-dependent tree network

Abstract

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ASJC Scopus subject areas

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