Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model.
Interior crises are understood as discontinuous changes of the size of a chaotic attractor that occur when an unstable periodic orbit collides with the chaotic attractor. We present here numerical evidence and theoretical reasoning which prove the existence of a chaos-chaos transition in which the c...
| Autor: | |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2003 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/21866 |
| Acceso en línea: | https://hdl.handle.net/2445/21866 |
| Access Level: | acceso abierto |
| Palabra clave: | Biofísica Física mèdica Física estadística Termodinàmica Sistemes dinàmics diferenciables Biophysics Medical physics Statistical physics Thermodynamics Differentiable dynamical systems |
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Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model.González-Miranda, J. M. (Jesús Manuel)BiofísicaFísica mèdicaFísica estadísticaTermodinàmicaSistemes dinàmics diferenciablesBiophysicsMedical physicsStatistical physicsThermodynamicsDifferentiable dynamical systemsInterior crises are understood as discontinuous changes of the size of a chaotic attractor that occur when an unstable periodic orbit collides with the chaotic attractor. We present here numerical evidence and theoretical reasoning which prove the existence of a chaos-chaos transition in which the change of the attractor size is sudden but continuous. This occurs in the Hindmarsh¿Rose model of a neuron, at the transition point between the bursting and spiking dynamics, which are two different dynamic behaviors that this system is able to present. Moreover, besides the change in attractor size, other significant properties of the system undergoing the transitions do change in a relevant qualitative way. The mechanism for such transition is understood in terms of a simple one-dimensional map whose dynamics undergoes a crossover between two different universal behaviorsAmerican Institute of Physics201220122003info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion8 p.application/pdfhttps://hdl.handle.net/2445/21866Articles publicats en revistes (Física de la Matèria Condensada)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésReproducció del document publicat a: http://dx.doi.org/10.1063/1.1594851Chaos, 2003, vol. 13, núm. 3, p. 845-852http://dx.doi.org/10.1063/1.1594851(c) American Institute of Physics, 2003info:eu-repo/semantics/openAccessoai:recercat.cat:2445/218662026-05-29T05:05:01Z |
| dc.title.none.fl_str_mv |
Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model. |
| title |
Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model. |
| spellingShingle |
Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model. González-Miranda, J. M. (Jesús Manuel) Biofísica Física mèdica Física estadística Termodinàmica Sistemes dinàmics diferenciables Biophysics Medical physics Statistical physics Thermodynamics Differentiable dynamical systems |
| title_short |
Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model. |
| title_full |
Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model. |
| title_fullStr |
Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model. |
| title_full_unstemmed |
Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model. |
| title_sort |
Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model. |
| dc.creator.none.fl_str_mv |
González-Miranda, J. M. (Jesús Manuel) |
| author |
González-Miranda, J. M. (Jesús Manuel) |
| author_facet |
González-Miranda, J. M. (Jesús Manuel) |
| author_role |
author |
| dc.subject.none.fl_str_mv |
Biofísica Física mèdica Física estadística Termodinàmica Sistemes dinàmics diferenciables Biophysics Medical physics Statistical physics Thermodynamics Differentiable dynamical systems |
| topic |
Biofísica Física mèdica Física estadística Termodinàmica Sistemes dinàmics diferenciables Biophysics Medical physics Statistical physics Thermodynamics Differentiable dynamical systems |
| description |
Interior crises are understood as discontinuous changes of the size of a chaotic attractor that occur when an unstable periodic orbit collides with the chaotic attractor. We present here numerical evidence and theoretical reasoning which prove the existence of a chaos-chaos transition in which the change of the attractor size is sudden but continuous. This occurs in the Hindmarsh¿Rose model of a neuron, at the transition point between the bursting and spiking dynamics, which are two different dynamic behaviors that this system is able to present. Moreover, besides the change in attractor size, other significant properties of the system undergoing the transitions do change in a relevant qualitative way. The mechanism for such transition is understood in terms of a simple one-dimensional map whose dynamics undergoes a crossover between two different universal behaviors |
| publishDate |
2003 |
| dc.date.none.fl_str_mv |
2003 2012 2012 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/2445/21866 |
| url |
https://hdl.handle.net/2445/21866 |
| dc.language.none.fl_str_mv |
Inglés |
| language_invalid_str_mv |
Inglés |
| dc.relation.none.fl_str_mv |
Reproducció del document publicat a: http://dx.doi.org/10.1063/1.1594851 Chaos, 2003, vol. 13, núm. 3, p. 845-852 http://dx.doi.org/10.1063/1.1594851 |
| dc.rights.none.fl_str_mv |
(c) American Institute of Physics, 2003 info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
(c) American Institute of Physics, 2003 |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
8 p. application/pdf |
| dc.publisher.none.fl_str_mv |
American Institute of Physics |
| publisher.none.fl_str_mv |
American Institute of Physics |
| dc.source.none.fl_str_mv |
Articles publicats en revistes (Física de la Matèria Condensada) reponame:Recercat. Dipósit de la Recerca de Catalunya instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
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Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| reponame_str |
Recercat. Dipósit de la Recerca de Catalunya |
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Recercat. Dipósit de la Recerca de Catalunya |
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1869411718569918464 |
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15,811543 |