A Cubic Memristive System with Two Twin Rössler-Type Chaotic Attractors Symmetrical About an Invariant Plane
Autor(a) principal: | |
---|---|
Data de Publicação: | 2022 |
Outros Autores: | , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1142/S0218127422300324 http://hdl.handle.net/11449/249391 |
Resumo: | Memristive circuits and systems have been widely studied in the last years due to their potential applications in several technological areas. They are capable of producing nonlinear periodic and chaotic oscillations, due to their locally-active characteristics. In this paper, we consider a cubic four-parameter differential system which models a memristive circuit consisting of three elements: a passive linear inductor, a passive linear capacitor and a locally-active current-controlled generic memristor. This system has a saddle-focus equilibrium point at the origin, whose global stable and unstable manifolds are, respectively, the x-axis and the plane x = 0, which are invariant sets where the dynamic is linear. We show that this structure can generate two twin Rössler-type chaotic attractors symmetrical with respect to the plane x = 0. We describe the mechanism of creation of these chaotic attractors, showing that, although being similar to the Rössler attractor, the twin attractors presented here have simpler structural mechanism of formation, since the system has no homoclinic or heteroclinic orbits to the saddle-focus, as presented by the Rössler system. The studied memristive system has the rare property of having chaotic dynamics and an invariant plane with linear dynamic, which is quite different from other chaotic systems presented in the literature that have invariant surfaces filled by equilibrium points. We also present and discuss the electronic circuit implementation of the considered system and study its dynamics at infinity, via the Poincaré compactification, showing that all the solutions, except the ones contained in the plane x = 0, are bounded and cannot escape to infinity. |
id |
UNSP_2229ca221175c63d23b4a62a7be1a880 |
---|---|
oai_identifier_str |
oai:repositorio.unesp.br:11449/249391 |
network_acronym_str |
UNSP |
network_name_str |
Repositório Institucional da UNESP |
repository_id_str |
2946 |
spelling |
A Cubic Memristive System with Two Twin Rössler-Type Chaotic Attractors Symmetrical About an Invariant Planechaotic dynamicsdynamics at infinityelectronic circuit implementationinvariant algebraic surfaceMemristive circuitPoincaré compactificationRössler-type attractorMemristive circuits and systems have been widely studied in the last years due to their potential applications in several technological areas. They are capable of producing nonlinear periodic and chaotic oscillations, due to their locally-active characteristics. In this paper, we consider a cubic four-parameter differential system which models a memristive circuit consisting of three elements: a passive linear inductor, a passive linear capacitor and a locally-active current-controlled generic memristor. This system has a saddle-focus equilibrium point at the origin, whose global stable and unstable manifolds are, respectively, the x-axis and the plane x = 0, which are invariant sets where the dynamic is linear. We show that this structure can generate two twin Rössler-type chaotic attractors symmetrical with respect to the plane x = 0. We describe the mechanism of creation of these chaotic attractors, showing that, although being similar to the Rössler attractor, the twin attractors presented here have simpler structural mechanism of formation, since the system has no homoclinic or heteroclinic orbits to the saddle-focus, as presented by the Rössler system. The studied memristive system has the rare property of having chaotic dynamics and an invariant plane with linear dynamic, which is quite different from other chaotic systems presented in the literature that have invariant surfaces filled by equilibrium points. We also present and discuss the electronic circuit implementation of the considered system and study its dynamics at infinity, via the Poincaré compactification, showing that all the solutions, except the ones contained in the plane x = 0, are bounded and cannot escape to infinity.Department of Mathematics and Computer Science Faculty of Science and Technology São Paulo State University (UNESP), SPDepartment of Mathematics Federal University of Technology - Paraná (UTFPR), PRDepartment of Electrical and Electronics Engineering Bandirma Onyedi Eylul UniversityDepartment of Computer Engineering Faculty of Engineering Hitit UniversityDepartment of Mathematics and Computer Science Faculty of Science and Technology São Paulo State University (UNESP), SPUniversidade Estadual Paulista (UNESP)Federal University of Technology - Paraná (UTFPR)Bandirma Onyedi Eylul UniversityHitit UniversityMessias, Marcelo [UNESP]Meneguette, Messias [UNESP]De Carvalho Reinol, AlissonGokyildirim, AbdullahAkgül, Akif2023-07-29T15:14:49Z2023-07-29T15:14:49Z2022-10-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1142/S0218127422300324International Journal of Bifurcation and Chaos, v. 32, n. 13, 2022.0218-1274http://hdl.handle.net/11449/24939110.1142/S02181274223003242-s2.0-85142320465Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengInternational Journal of Bifurcation and Chaosinfo:eu-repo/semantics/openAccess2024-06-19T14:32:05Zoai:repositorio.unesp.br:11449/249391Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T20:23:36.118191Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
A Cubic Memristive System with Two Twin Rössler-Type Chaotic Attractors Symmetrical About an Invariant Plane |
title |
A Cubic Memristive System with Two Twin Rössler-Type Chaotic Attractors Symmetrical About an Invariant Plane |
spellingShingle |
A Cubic Memristive System with Two Twin Rössler-Type Chaotic Attractors Symmetrical About an Invariant Plane Messias, Marcelo [UNESP] chaotic dynamics dynamics at infinity electronic circuit implementation invariant algebraic surface Memristive circuit Poincaré compactification Rössler-type attractor |
title_short |
A Cubic Memristive System with Two Twin Rössler-Type Chaotic Attractors Symmetrical About an Invariant Plane |
title_full |
A Cubic Memristive System with Two Twin Rössler-Type Chaotic Attractors Symmetrical About an Invariant Plane |
title_fullStr |
A Cubic Memristive System with Two Twin Rössler-Type Chaotic Attractors Symmetrical About an Invariant Plane |
title_full_unstemmed |
A Cubic Memristive System with Two Twin Rössler-Type Chaotic Attractors Symmetrical About an Invariant Plane |
title_sort |
A Cubic Memristive System with Two Twin Rössler-Type Chaotic Attractors Symmetrical About an Invariant Plane |
author |
Messias, Marcelo [UNESP] |
author_facet |
Messias, Marcelo [UNESP] Meneguette, Messias [UNESP] De Carvalho Reinol, Alisson Gokyildirim, Abdullah Akgül, Akif |
author_role |
author |
author2 |
Meneguette, Messias [UNESP] De Carvalho Reinol, Alisson Gokyildirim, Abdullah Akgül, Akif |
author2_role |
author author author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) Federal University of Technology - Paraná (UTFPR) Bandirma Onyedi Eylul University Hitit University |
dc.contributor.author.fl_str_mv |
Messias, Marcelo [UNESP] Meneguette, Messias [UNESP] De Carvalho Reinol, Alisson Gokyildirim, Abdullah Akgül, Akif |
dc.subject.por.fl_str_mv |
chaotic dynamics dynamics at infinity electronic circuit implementation invariant algebraic surface Memristive circuit Poincaré compactification Rössler-type attractor |
topic |
chaotic dynamics dynamics at infinity electronic circuit implementation invariant algebraic surface Memristive circuit Poincaré compactification Rössler-type attractor |
description |
Memristive circuits and systems have been widely studied in the last years due to their potential applications in several technological areas. They are capable of producing nonlinear periodic and chaotic oscillations, due to their locally-active characteristics. In this paper, we consider a cubic four-parameter differential system which models a memristive circuit consisting of three elements: a passive linear inductor, a passive linear capacitor and a locally-active current-controlled generic memristor. This system has a saddle-focus equilibrium point at the origin, whose global stable and unstable manifolds are, respectively, the x-axis and the plane x = 0, which are invariant sets where the dynamic is linear. We show that this structure can generate two twin Rössler-type chaotic attractors symmetrical with respect to the plane x = 0. We describe the mechanism of creation of these chaotic attractors, showing that, although being similar to the Rössler attractor, the twin attractors presented here have simpler structural mechanism of formation, since the system has no homoclinic or heteroclinic orbits to the saddle-focus, as presented by the Rössler system. The studied memristive system has the rare property of having chaotic dynamics and an invariant plane with linear dynamic, which is quite different from other chaotic systems presented in the literature that have invariant surfaces filled by equilibrium points. We also present and discuss the electronic circuit implementation of the considered system and study its dynamics at infinity, via the Poincaré compactification, showing that all the solutions, except the ones contained in the plane x = 0, are bounded and cannot escape to infinity. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-10-01 2023-07-29T15:14:49Z 2023-07-29T15:14:49Z |
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 |
http://dx.doi.org/10.1142/S0218127422300324 International Journal of Bifurcation and Chaos, v. 32, n. 13, 2022. 0218-1274 http://hdl.handle.net/11449/249391 10.1142/S0218127422300324 2-s2.0-85142320465 |
url |
http://dx.doi.org/10.1142/S0218127422300324 http://hdl.handle.net/11449/249391 |
identifier_str_mv |
International Journal of Bifurcation and Chaos, v. 32, n. 13, 2022. 0218-1274 10.1142/S0218127422300324 2-s2.0-85142320465 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
International Journal of Bifurcation and Chaos |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129196384321536 |