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Solitary states in the mean-field limit

Kruk, N. and Maistrenko, Y. and Koeppl, H. (2020):
Solitary states in the mean-field limit.
In: Chaos: An Interdisciplinary Journal of Nonlinear Science, 30 (11), American Institute of Physics, ISSN 1054-1500,
DOI: 10.1063/5.0029585,
[Article]

Abstract

We study active matter systems where the orientational dynamics of underlying self-propelled particles obey second order equations. By primarily concentrating on a spatially homogeneous setup for particle distribution, our analysis combines theories of active matter and oscillatory networks. For such systems, we analyze the appearance of solitary states via a homoclinic bifurcation as a mechanism of the frequency clustering. By introducing noise, we establish a stochastic version of solitary states and derive the mean-field limit described by a partial differential equation for a one-particle probability density function, which one might call the continuum Kuramoto model with inertia and noise. By studying this limit, we establish second order phase transitions between polar order and disorder. The combination of both analytical and numerical approaches in our study demonstrates an excellent qualitative agreement between mean-field and finite size models.

Item Type: Article
Erschienen: 2020
Creators: Kruk, N. and Maistrenko, Y. and Koeppl, H.
Title: Solitary states in the mean-field limit
Language: English
Abstract:

We study active matter systems where the orientational dynamics of underlying self-propelled particles obey second order equations. By primarily concentrating on a spatially homogeneous setup for particle distribution, our analysis combines theories of active matter and oscillatory networks. For such systems, we analyze the appearance of solitary states via a homoclinic bifurcation as a mechanism of the frequency clustering. By introducing noise, we establish a stochastic version of solitary states and derive the mean-field limit described by a partial differential equation for a one-particle probability density function, which one might call the continuum Kuramoto model with inertia and noise. By studying this limit, we establish second order phase transitions between polar order and disorder. The combination of both analytical and numerical approaches in our study demonstrates an excellent qualitative agreement between mean-field and finite size models.

Journal or Publication Title: Chaos: An Interdisciplinary Journal of Nonlinear Science
Journal volume: 30
Number: 11
Publisher: American Institute of Physics
Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications
Date Deposited: 09 Nov 2020 12:16
DOI: 10.1063/5.0029585
Additional Information:

Art. 111104

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