Multistability in a star network of Kuramoto-type oscillators with synaptic plasticity

Abstract We analyze multistability in a star-type network of phase oscillators with coupling weights governed by phase-difference-dependent plasticity. It is shown that a network with N leaves can evolve into $$2^N$$ 2 N various asymptotic states, characterized by different values of the coupling st...

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Autores principales:	Irmantas Ratas, Kestutis Pyragas, Peter A. Tass
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/4bc9515fdf454cf8b90e49aea55d6483
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spelling	oai:doaj.org-article:4bc9515fdf454cf8b90e49aea55d64832021-12-02T17:01:57ZMultistability in a star network of Kuramoto-type oscillators with synaptic plasticity10.1038/s41598-021-89198-02045-2322https://doaj.org/article/4bc9515fdf454cf8b90e49aea55d64832021-05-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-89198-0https://doaj.org/toc/2045-2322Abstract We analyze multistability in a star-type network of phase oscillators with coupling weights governed by phase-difference-dependent plasticity. It is shown that a network with N leaves can evolve into $$2^N$$ 2 N various asymptotic states, characterized by different values of the coupling strength between the hub and the leaves. Starting from the simple case of two coupled oscillators, we develop an analytical approach based on two small parameters $$\varepsilon$$ ε and $$\mu$$ μ , where $$\varepsilon$$ ε is the ratio of the time scales of the phase variables and synaptic weights, and $$\mu$$ μ defines the sharpness of the plasticity boundary function. The limit $$\mu \rightarrow 0$$ μ → 0 corresponds to a hard boundary. The analytical results obtained on the model of two oscillators are generalized for multi-leaf star networks. Multistability with $$2^N$$ 2 N various asymptotic states is numerically demonstrated for one-, two-, three- and nine-leaf star-type networks.Irmantas RatasKestutis PyragasPeter A. TassNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-15 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Irmantas Ratas Kestutis Pyragas Peter A. Tass Multistability in a star network of Kuramoto-type oscillators with synaptic plasticity
description	Abstract We analyze multistability in a star-type network of phase oscillators with coupling weights governed by phase-difference-dependent plasticity. It is shown that a network with N leaves can evolve into $$2^N$$ 2 N various asymptotic states, characterized by different values of the coupling strength between the hub and the leaves. Starting from the simple case of two coupled oscillators, we develop an analytical approach based on two small parameters $$\varepsilon$$ ε and $$\mu$$ μ , where $$\varepsilon$$ ε is the ratio of the time scales of the phase variables and synaptic weights, and $$\mu$$ μ defines the sharpness of the plasticity boundary function. The limit $$\mu \rightarrow 0$$ μ → 0 corresponds to a hard boundary. The analytical results obtained on the model of two oscillators are generalized for multi-leaf star networks. Multistability with $$2^N$$ 2 N various asymptotic states is numerically demonstrated for one-, two-, three- and nine-leaf star-type networks.
format	article
author	Irmantas Ratas Kestutis Pyragas Peter A. Tass
author_facet	Irmantas Ratas Kestutis Pyragas Peter A. Tass
author_sort	Irmantas Ratas
title	Multistability in a star network of Kuramoto-type oscillators with synaptic plasticity
title_short	Multistability in a star network of Kuramoto-type oscillators with synaptic plasticity
title_full	Multistability in a star network of Kuramoto-type oscillators with synaptic plasticity
title_fullStr	Multistability in a star network of Kuramoto-type oscillators with synaptic plasticity
title_full_unstemmed	Multistability in a star network of Kuramoto-type oscillators with synaptic plasticity
title_sort	multistability in a star network of kuramoto-type oscillators with synaptic plasticity
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/4bc9515fdf454cf8b90e49aea55d6483
work_keys_str_mv	AT irmantasratas multistabilityinastarnetworkofkuramototypeoscillatorswithsynapticplasticity AT kestutispyragas multistabilityinastarnetworkofkuramototypeoscillatorswithsynapticplasticity AT peteratass multistabilityinastarnetworkofkuramototypeoscillatorswithsynapticplasticity
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Multistability in a star network of Kuramoto-type oscillators with synaptic plasticity

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