Triple point of synchronization, phase singularity, and excitability along the transition between unbounded and bounded phase oscillations in a forced nonlinear oscillator
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/222846 |
Resumo: | We report the discovery of a codimension-two phenomenon in the phase diagram of a second-order self sustained nonlinear oscillator subject to a constant external periodic forcing, around which three regimes associated with the synchronization phenomenon exist, namely phase-locking, frequency-locking without phase-locking, and frequency-unlocking states. The triple point of synchronization arises when a saddle-node homoclinic cycle collides with the zero-amplitude state of the forced oscillator. A line on the phase diagram where limit-cycle solutions contain a phase singularity departs from the triple point, giving rise to a codimension one transition between the regimes of frequency unlocking and frequency locking without phase locking. At the parameter values where the critical transition occurs, the forced oscillator exhibits a separatrix with a π phase jump, i.e., a particular trajectory in phase space that separates two distinct behaviors of the phase dynamics. Close to the triple point, noise induces excitable pulses where the two variants of type-I excitability, i.e., pulses with and without 2π phase slips, appear stochastically. The impacts of weak noise and some other dynamical aspects associated with the transition induced by the singular phenomenon are also discussed. |
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Prants, Willian TiagoBonatto, Cristian2021-06-25T04:25:31Z20211539-3755http://hdl.handle.net/10183/222846001125700We report the discovery of a codimension-two phenomenon in the phase diagram of a second-order self sustained nonlinear oscillator subject to a constant external periodic forcing, around which three regimes associated with the synchronization phenomenon exist, namely phase-locking, frequency-locking without phase-locking, and frequency-unlocking states. The triple point of synchronization arises when a saddle-node homoclinic cycle collides with the zero-amplitude state of the forced oscillator. A line on the phase diagram where limit-cycle solutions contain a phase singularity departs from the triple point, giving rise to a codimension one transition between the regimes of frequency unlocking and frequency locking without phase locking. At the parameter values where the critical transition occurs, the forced oscillator exhibits a separatrix with a π phase jump, i.e., a particular trajectory in phase space that separates two distinct behaviors of the phase dynamics. Close to the triple point, noise induces excitable pulses where the two variants of type-I excitability, i.e., pulses with and without 2π phase slips, appear stochastically. The impacts of weak noise and some other dynamical aspects associated with the transition induced by the singular phenomenon are also discussed.application/pdfengPhysical review. E, Statistical, nonlinear, and soft matter physics. Melville. Vol. 103, no. 3 (Mar. 2021), 032201, 13 p.Diagramas de faseOscilações não-linearesDinâmica não-linearTriple point of synchronization, phase singularity, and excitability along the transition between unbounded and bounded phase oscillations in a forced nonlinear oscillatorEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT001125700.pdf.txt001125700.pdf.txtExtracted Texttext/plain66873http://www.lume.ufrgs.br/bitstream/10183/222846/2/001125700.pdf.txt1bdf0d21c6a3a78ecfa8405f0c1c7471MD52ORIGINAL001125700.pdfTexto completo (inglês)application/pdf2813921http://www.lume.ufrgs.br/bitstream/10183/222846/1/001125700.pdfb5cbd81f2f8fd3dbcf7e9af1f9db7869MD5110183/2228462023-08-12 03:48:39.11588oai:www.lume.ufrgs.br:10183/222846Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2023-08-12T06:48:39Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Triple point of synchronization, phase singularity, and excitability along the transition between unbounded and bounded phase oscillations in a forced nonlinear oscillator |
title |
Triple point of synchronization, phase singularity, and excitability along the transition between unbounded and bounded phase oscillations in a forced nonlinear oscillator |
spellingShingle |
Triple point of synchronization, phase singularity, and excitability along the transition between unbounded and bounded phase oscillations in a forced nonlinear oscillator Prants, Willian Tiago Diagramas de fase Oscilações não-lineares Dinâmica não-linear |
title_short |
Triple point of synchronization, phase singularity, and excitability along the transition between unbounded and bounded phase oscillations in a forced nonlinear oscillator |
title_full |
Triple point of synchronization, phase singularity, and excitability along the transition between unbounded and bounded phase oscillations in a forced nonlinear oscillator |
title_fullStr |
Triple point of synchronization, phase singularity, and excitability along the transition between unbounded and bounded phase oscillations in a forced nonlinear oscillator |
title_full_unstemmed |
Triple point of synchronization, phase singularity, and excitability along the transition between unbounded and bounded phase oscillations in a forced nonlinear oscillator |
title_sort |
Triple point of synchronization, phase singularity, and excitability along the transition between unbounded and bounded phase oscillations in a forced nonlinear oscillator |
author |
Prants, Willian Tiago |
author_facet |
Prants, Willian Tiago Bonatto, Cristian |
author_role |
author |
author2 |
Bonatto, Cristian |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Prants, Willian Tiago Bonatto, Cristian |
dc.subject.por.fl_str_mv |
Diagramas de fase Oscilações não-lineares Dinâmica não-linear |
topic |
Diagramas de fase Oscilações não-lineares Dinâmica não-linear |
description |
We report the discovery of a codimension-two phenomenon in the phase diagram of a second-order self sustained nonlinear oscillator subject to a constant external periodic forcing, around which three regimes associated with the synchronization phenomenon exist, namely phase-locking, frequency-locking without phase-locking, and frequency-unlocking states. The triple point of synchronization arises when a saddle-node homoclinic cycle collides with the zero-amplitude state of the forced oscillator. A line on the phase diagram where limit-cycle solutions contain a phase singularity departs from the triple point, giving rise to a codimension one transition between the regimes of frequency unlocking and frequency locking without phase locking. At the parameter values where the critical transition occurs, the forced oscillator exhibits a separatrix with a π phase jump, i.e., a particular trajectory in phase space that separates two distinct behaviors of the phase dynamics. Close to the triple point, noise induces excitable pulses where the two variants of type-I excitability, i.e., pulses with and without 2π phase slips, appear stochastically. The impacts of weak noise and some other dynamical aspects associated with the transition induced by the singular phenomenon are also discussed. |
publishDate |
2021 |
dc.date.accessioned.fl_str_mv |
2021-06-25T04:25:31Z |
dc.date.issued.fl_str_mv |
2021 |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10183/222846 |
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1539-3755 |
dc.identifier.nrb.pt_BR.fl_str_mv |
001125700 |
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1539-3755 001125700 |
url |
http://hdl.handle.net/10183/222846 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Physical review. E, Statistical, nonlinear, and soft matter physics. Melville. Vol. 103, no. 3 (Mar. 2021), 032201, 13 p. |
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info:eu-repo/semantics/openAccess |
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openAccess |
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