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On the dynamics of a Van der Pol–Duffing snap system

Bibliographic Details
Main Author: Wiggers V.*
Publication Date: 2022
Other Authors: Rech P.C.*
Format: Article
Language: eng
Source: Repositório Institucional da Udesc
dARK ID: ark:/33523/001300000btk3
Download full: https://repositorio.udesc.br/handle/UDESC/3096
Summary: © 2022, The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.Abstract: In this paper, we propose an autonomous snap oscillator which was obtained from the Van der Pol–Duffing forced oscillator. The proposed system presents polynomial nonlinearities, being modeled by a four-parameter fourth-order ordinary differential equation. We investigate the dynamics of this system. More specifically, keeping two of the parameters fixed, we investigate numerically the organization of chaos and periodicity in this system, using an appropriately chosen parameter plane. We show that such parameter plane presents parameters regions for which the multistability phenomenon is perfectly characterized. Plots of basins of attraction and coexisting attractors are presented. An analytical investigation regarding the stability of equilibrium points was also carried out. Graphic abstract: [Figure not available: see fulltext.]
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spelling On the dynamics of a Van der Pol–Duffing snap system© 2022, The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.Abstract: In this paper, we propose an autonomous snap oscillator which was obtained from the Van der Pol–Duffing forced oscillator. The proposed system presents polynomial nonlinearities, being modeled by a four-parameter fourth-order ordinary differential equation. We investigate the dynamics of this system. More specifically, keeping two of the parameters fixed, we investigate numerically the organization of chaos and periodicity in this system, using an appropriately chosen parameter plane. We show that such parameter plane presents parameters regions for which the multistability phenomenon is perfectly characterized. Plots of basins of attraction and coexisting attractors are presented. An analytical investigation regarding the stability of equilibrium points was also carried out. Graphic abstract: [Figure not available: see fulltext.]2024-12-05T22:56:44Z2022info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1434-603610.1140/epjb/s10051-022-00294-0https://repositorio.udesc.br/handle/UDESC/3096ark:/33523/001300000btk3European Physical Journal B952Wiggers V.*Rech P.C.*engreponame:Repositório Institucional da Udescinstname:Universidade do Estado de Santa Catarina (UDESC)instacron:UDESCinfo:eu-repo/semantics/openAccess2024-12-07T20:40:44Zoai:repositorio.udesc.br:UDESC/3096Biblioteca Digital de Teses e Dissertaçõeshttps://pergamumweb.udesc.br/biblioteca/index.phpPRIhttps://repositorio-api.udesc.br/server/oai/requestri@udesc.bropendoar:63912024-12-07T20:40:44Repositório Institucional da Udesc - Universidade do Estado de Santa Catarina (UDESC)false
dc.title.none.fl_str_mv On the dynamics of a Van der Pol–Duffing snap system
title On the dynamics of a Van der Pol–Duffing snap system
spellingShingle On the dynamics of a Van der Pol–Duffing snap system
Wiggers V.*
title_short On the dynamics of a Van der Pol–Duffing snap system
title_full On the dynamics of a Van der Pol–Duffing snap system
title_fullStr On the dynamics of a Van der Pol–Duffing snap system
title_full_unstemmed On the dynamics of a Van der Pol–Duffing snap system
title_sort On the dynamics of a Van der Pol–Duffing snap system
author Wiggers V.*
author_facet Wiggers V.*
Rech P.C.*
author_role author
author2 Rech P.C.*
author2_role author
dc.contributor.author.fl_str_mv Wiggers V.*
Rech P.C.*
description © 2022, The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.Abstract: In this paper, we propose an autonomous snap oscillator which was obtained from the Van der Pol–Duffing forced oscillator. The proposed system presents polynomial nonlinearities, being modeled by a four-parameter fourth-order ordinary differential equation. We investigate the dynamics of this system. More specifically, keeping two of the parameters fixed, we investigate numerically the organization of chaos and periodicity in this system, using an appropriately chosen parameter plane. We show that such parameter plane presents parameters regions for which the multistability phenomenon is perfectly characterized. Plots of basins of attraction and coexisting attractors are presented. An analytical investigation regarding the stability of equilibrium points was also carried out. Graphic abstract: [Figure not available: see fulltext.]
publishDate 2022
dc.date.none.fl_str_mv 2022
2024-12-05T22:56:44Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv 1434-6036
10.1140/epjb/s10051-022-00294-0
https://repositorio.udesc.br/handle/UDESC/3096
dc.identifier.dark.fl_str_mv ark:/33523/001300000btk3
identifier_str_mv 1434-6036
10.1140/epjb/s10051-022-00294-0
ark:/33523/001300000btk3
url https://repositorio.udesc.br/handle/UDESC/3096
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv European Physical Journal B
95
2
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv reponame:Repositório Institucional da Udesc
instname:Universidade do Estado de Santa Catarina (UDESC)
instacron:UDESC
instname_str Universidade do Estado de Santa Catarina (UDESC)
instacron_str UDESC
institution UDESC
reponame_str Repositório Institucional da Udesc
collection Repositório Institucional da Udesc
repository.name.fl_str_mv Repositório Institucional da Udesc - Universidade do Estado de Santa Catarina (UDESC)
repository.mail.fl_str_mv ri@udesc.br
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