Continuum limit of the adaptive Kuramoto model
Cestnik, Rok LU and Martens, Erik A. LU
(2025)
In Chaos
35(1).
- Abstract
We investigate the dynamics of the adaptive Kuramoto model with slow adaptation in the continuum limit, N → ∞ . This model is distinguished by dense multistability, where multiple states coexist for the same system parameters. The underlying cause of this multistability is that some oscillators can lock at different phases or switch between locking and drifting depending on their initial conditions. We identify new states, such as two-cluster states. To simplify the analysis, we introduce an approximate reduction of the model via row-averaging of the coupling matrix. We derive a self-consistency equation for the reduced model and present a stability diagram illustrating the effects of positive and negative adaptation. Our theoretical... (More)
We investigate the dynamics of the adaptive Kuramoto model with slow adaptation in the continuum limit, N → ∞ . This model is distinguished by dense multistability, where multiple states coexist for the same system parameters. The underlying cause of this multistability is that some oscillators can lock at different phases or switch between locking and drifting depending on their initial conditions. We identify new states, such as two-cluster states. To simplify the analysis, we introduce an approximate reduction of the model via row-averaging of the coupling matrix. We derive a self-consistency equation for the reduced model and present a stability diagram illustrating the effects of positive and negative adaptation. Our theoretical findings are validated through numerical simulations of a large finite system. Comparisons of previous work highlight the significant influence of adaptation on synchronization behavior.
(Less)
- author
- Cestnik, Rok
LU
and Martens, Erik A.
LU
- organization
- publishing date
- 2025-01-01
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Chaos
- volume
- 35
- issue
- 1
- article number
- 013109
- publisher
- American Institute of Physics (AIP)
- external identifiers
-
- scopus:85214589894
- pmid:39752200
- ISSN
- 1054-1500
- DOI
- 10.1063/5.0226759
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2025 Author(s).
- id
- cb236a49-a6bf-4936-b90a-2ad4fcb03714
- date added to LUP
- 2025-02-03 08:12:35
- date last changed
- 2025-07-07 20:29:01
@article{cb236a49-a6bf-4936-b90a-2ad4fcb03714,
abstract = {{<p>We investigate the dynamics of the adaptive Kuramoto model with slow adaptation in the continuum limit, N → ∞ . This model is distinguished by dense multistability, where multiple states coexist for the same system parameters. The underlying cause of this multistability is that some oscillators can lock at different phases or switch between locking and drifting depending on their initial conditions. We identify new states, such as two-cluster states. To simplify the analysis, we introduce an approximate reduction of the model via row-averaging of the coupling matrix. We derive a self-consistency equation for the reduced model and present a stability diagram illustrating the effects of positive and negative adaptation. Our theoretical findings are validated through numerical simulations of a large finite system. Comparisons of previous work highlight the significant influence of adaptation on synchronization behavior.</p>}},
author = {{Cestnik, Rok and Martens, Erik A.}},
issn = {{1054-1500}},
language = {{eng}},
month = {{01}},
number = {{1}},
publisher = {{American Institute of Physics (AIP)}},
series = {{Chaos}},
title = {{Continuum limit of the adaptive Kuramoto model}},
url = {{http://dx.doi.org/10.1063/5.0226759}},
doi = {{10.1063/5.0226759}},
volume = {{35}},
year = {{2025}},
}