Inhibition-based relaxation oscillations emerge in resonator networks

Autores
Bel, Andrea Liliana; Torresi, Ana María Luján; Rotstein, Horacio
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We investigate the mechanisms responsible for the generation of oscillations in mutually inhibitory cells of non-oscillatory neurons and the transitions from non-relaxation (sinusoidal-like) oscillations to relaxation oscillations. We use a minimal model consisting of a 2D linear resonator, a 1D linear cell and graded synaptic inhibition described by a piecewise linear sigmoidal function. Individually, resonators exhibit a peak in their response to oscillatory inputs at a preferred (resonant) frequency, but they do not show intrinsic (damped) oscillations in response to constant perturbations. We show that network oscillations emerge in this model for appropriate balance of the model parameters, particularly the connectivity strength and the steepness of the connectivity function. For fixed values of the latter, there is a transition from sinusoidal-like to relaxation oscillations as the connectivity strength increases. Similarly, for fixed connectivity strength values, increasing the connectivity steepness also leads to relaxation oscillations. Interestingly, relaxation oscillations are not observed when the 2D linear node is a damped oscillator. We discuss the role of the intrinsic properties of the participating nodes by focusing on the effect that the resonator’s resonant frequency has on the network frequency and amplitude.
Fil: Bel, Andrea Liliana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Torresi, Ana María Luján. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Rotstein, Horacio. Rutgers University; Estados Unidos
Materia
NEURAL NETWORKS
RESONANCE
RELAXATION OSCILLATION
CANARD PHENOMENON
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/112002
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/112002
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Inhibition-based relaxation oscillations emerge in resonator networksBel, Andrea LilianaTorresi, Ana María LujánRotstein, HoracioNEURAL NETWORKSRESONANCERELAXATION OSCILLATIONCANARD PHENOMENONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We investigate the mechanisms responsible for the generation of oscillations in mutually inhibitory cells of non-oscillatory neurons and the transitions from non-relaxation (sinusoidal-like) oscillations to relaxation oscillations. We use a minimal model consisting of a 2D linear resonator, a 1D linear cell and graded synaptic inhibition described by a piecewise linear sigmoidal function. Individually, resonators exhibit a peak in their response to oscillatory inputs at a preferred (resonant) frequency, but they do not show intrinsic (damped) oscillations in response to constant perturbations. We show that network oscillations emerge in this model for appropriate balance of the model parameters, particularly the connectivity strength and the steepness of the connectivity function. For fixed values of the latter, there is a transition from sinusoidal-like to relaxation oscillations as the connectivity strength increases. Similarly, for fixed connectivity strength values, increasing the connectivity steepness also leads to relaxation oscillations. Interestingly, relaxation oscillations are not observed when the 2D linear node is a damped oscillator. We discuss the role of the intrinsic properties of the participating nodes by focusing on the effect that the resonator’s resonant frequency has on the network frequency and amplitude.Fil: Bel, Andrea Liliana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Torresi, Ana María Luján. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Rotstein, Horacio. Rutgers University; Estados UnidosEDP Sciences2019-05-27info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/112002Bel, Andrea Liliana; Torresi, Ana María Luján; Rotstein, Horacio; Inhibition-based relaxation oscillations emerge in resonator networks; EDP Sciences; Mathematical Modelling of Natural Phenomena; 14; 4; 27-5-2019; 1-280973-53481760-6101CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.mmnp-journal.org/10.1051/mmnp/2019019info:eu-repo/semantics/altIdentifier/doi/10.1051/mmnp/2019019info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:17:48Zoai:ri.conicet.gov.ar:11336/112002instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:17:49.268CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Inhibition-based relaxation oscillations emerge in resonator networks
title Inhibition-based relaxation oscillations emerge in resonator networks
spellingShingle Inhibition-based relaxation oscillations emerge in resonator networks
Bel, Andrea Liliana
NEURAL NETWORKS
RESONANCE
RELAXATION OSCILLATION
CANARD PHENOMENON
title_short Inhibition-based relaxation oscillations emerge in resonator networks
title_full Inhibition-based relaxation oscillations emerge in resonator networks
title_fullStr Inhibition-based relaxation oscillations emerge in resonator networks
title_full_unstemmed Inhibition-based relaxation oscillations emerge in resonator networks
title_sort Inhibition-based relaxation oscillations emerge in resonator networks
dc.creator.none.fl_str_mv Bel, Andrea Liliana
Torresi, Ana María Luján
Rotstein, Horacio
author Bel, Andrea Liliana
author_facet Bel, Andrea Liliana
Torresi, Ana María Luján
Rotstein, Horacio
author_role author
author2 Torresi, Ana María Luján
Rotstein, Horacio
author2_role author
author
dc.subject.none.fl_str_mv NEURAL NETWORKS
RESONANCE
RELAXATION OSCILLATION
CANARD PHENOMENON
topic NEURAL NETWORKS
RESONANCE
RELAXATION OSCILLATION
CANARD PHENOMENON
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We investigate the mechanisms responsible for the generation of oscillations in mutually inhibitory cells of non-oscillatory neurons and the transitions from non-relaxation (sinusoidal-like) oscillations to relaxation oscillations. We use a minimal model consisting of a 2D linear resonator, a 1D linear cell and graded synaptic inhibition described by a piecewise linear sigmoidal function. Individually, resonators exhibit a peak in their response to oscillatory inputs at a preferred (resonant) frequency, but they do not show intrinsic (damped) oscillations in response to constant perturbations. We show that network oscillations emerge in this model for appropriate balance of the model parameters, particularly the connectivity strength and the steepness of the connectivity function. For fixed values of the latter, there is a transition from sinusoidal-like to relaxation oscillations as the connectivity strength increases. Similarly, for fixed connectivity strength values, increasing the connectivity steepness also leads to relaxation oscillations. Interestingly, relaxation oscillations are not observed when the 2D linear node is a damped oscillator. We discuss the role of the intrinsic properties of the participating nodes by focusing on the effect that the resonator’s resonant frequency has on the network frequency and amplitude.
Fil: Bel, Andrea Liliana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Torresi, Ana María Luján. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Rotstein, Horacio. Rutgers University; Estados Unidos
description We investigate the mechanisms responsible for the generation of oscillations in mutually inhibitory cells of non-oscillatory neurons and the transitions from non-relaxation (sinusoidal-like) oscillations to relaxation oscillations. We use a minimal model consisting of a 2D linear resonator, a 1D linear cell and graded synaptic inhibition described by a piecewise linear sigmoidal function. Individually, resonators exhibit a peak in their response to oscillatory inputs at a preferred (resonant) frequency, but they do not show intrinsic (damped) oscillations in response to constant perturbations. We show that network oscillations emerge in this model for appropriate balance of the model parameters, particularly the connectivity strength and the steepness of the connectivity function. For fixed values of the latter, there is a transition from sinusoidal-like to relaxation oscillations as the connectivity strength increases. Similarly, for fixed connectivity strength values, increasing the connectivity steepness also leads to relaxation oscillations. Interestingly, relaxation oscillations are not observed when the 2D linear node is a damped oscillator. We discuss the role of the intrinsic properties of the participating nodes by focusing on the effect that the resonator’s resonant frequency has on the network frequency and amplitude.
publishDate 2019
dc.date.none.fl_str_mv 2019-05-27
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/112002
Bel, Andrea Liliana; Torresi, Ana María Luján; Rotstein, Horacio; Inhibition-based relaxation oscillations emerge in resonator networks; EDP Sciences; Mathematical Modelling of Natural Phenomena; 14; 4; 27-5-2019; 1-28
0973-5348
1760-6101
CONICET Digital
CONICET
url http://hdl.handle.net/11336/112002
identifier_str_mv Bel, Andrea Liliana; Torresi, Ana María Luján; Rotstein, Horacio; Inhibition-based relaxation oscillations emerge in resonator networks; EDP Sciences; Mathematical Modelling of Natural Phenomena; 14; 4; 27-5-2019; 1-28
0973-5348
1760-6101
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.mmnp-journal.org/10.1051/mmnp/2019019
info:eu-repo/semantics/altIdentifier/doi/10.1051/mmnp/2019019
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv EDP Sciences
publisher.none.fl_str_mv EDP Sciences
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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