The Lorenz chaotic systems as nonlinear oscillators with memory
Nonlinear dynamical systems (systems of 1st order ordinary differential equations) capable of generating chaos are analytically nonintegrable. Despite of this fact, analytical tools can be used to extract useful information. In this paper the original Lorenz system and its modifications are reduced...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2009 |
| País: | México |
| Institución: | UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO |
| Repositorio: | Atmósfera |
| Idioma: | inglés |
| OAI Identifier: | oai:ojs.pkp.sfu.ca:article/8527 |
| Acceso en línea: | https://www.revistascca.unam.mx/atm/index.php/atm/article/view/8527 |
| Access Level: | acceso abierto |
| Palabra clave: | CHAOTIC SYSTEMS MEMORY FUNCTION DUFFING OSCILLATOR Chaotic systems memory function duffing oscillator |
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The Lorenz chaotic systems as nonlinear oscillators with memoryThe Lorenz chaotic systems as nonlinear oscillators with memoryPANCHEV, S.SPASSOVA, T.CHAOTIC SYSTEMSMEMORY FUNCTIONDUFFING OSCILLATORChaotic systemsmemory functionduffing oscillatorNonlinear dynamical systems (systems of 1st order ordinary differential equations) capable of generating chaos are analytically nonintegrable. Despite of this fact, analytical tools can be used to extract useful information. In this paper the original Lorenz system and its modifications are reduced to single oscillatory type integral-differential equations with delayed argument. This yields to appearance of an ‘‘endogenous’’ term interpreted as memory for the past. Moreover, the equations are valid far from the initial instant (theoretically at t→∞), when the system eventually evolves on its attractor set. This corresponds to the numerical solutions when an appropriate initial part of the iterates is usually discarded to eliminate the transients. Besides, the form of the equations allows statistical treatment.LOS SISTEMAS NO LINEARES DINÁMICOS (SISTEMAS DE ECUACIONES DIFERENCIALES ORDINARIAS DE 1ER ORDEN) CAPACES DE GENERAR CAOS SON NO INTEGRABLES ANALÍTICAMENTE. A PESAR DE ESTO, SE PUEDEN UTILIZAR HERRAMIENTAS ANALÍTICAS PARA EXTRAER INFORMACIÓN ÚTIL DE ELLAS. EN ESTE TRABAJO EL SISTEMA ORIGINAL DE LORENZ Y SUS MODIFICACIONES SE REDUCEN A ECUACIONES OSCILATORIAS ÚNICAS DE TIPO INTEGRAL-DIFERENCIAL CON ARGUMENTO RETRASADO. ESTO LLEVA A LA APARICIÓN DE UN TERMINO ""ENDÓGENO"" QUE SE INTERPRETA COMO MEMORIA PARA EL PASADO. POR OTRA PARTE, LAS ECUACIONES SON VALIDAS MAS ALLA DEL INSTANTE INICIAL (TEÓRICAMENTE EN T), CUANDO EL SISTEMA EVOLUCIONA HACIA SU CONJUNTO ATRACTOR. ESTO CORRESPONDE A LAS SOLUCIONES NUMÉRICAS CUANDO UNA PARTE INICIAL ADECUADA DEL ITERATO GENERALMENTE SE DESCARTA PARA ELIMINAR A LOS TRANSITORIOS. ADEMÁS LA FORMA DE LAS ECUACIONES PERMITE SU TRATAMIENTO ESTADÍSTICO.Instituto de Ciencias de la Atmósfera y Cambio Climático, Universidad Nacional Autónoma de México2009-10-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://www.revistascca.unam.mx/atm/index.php/atm/article/view/8527Atmósfera; Vol. 17 Núm. 3 (2004)Atmósfera; Vol. 17 No. 3 (2004)2395-88120187-6236reponame:Atmósferainstname:UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICOinstacron:UNAMenghttps://www.revistascca.unam.mx/atm/index.php/atm/article/view/8527/7997info:eu-repo/semantics/openAccessoai:ojs.pkp.sfu.ca:article/85272024-08-16T16:52:34Z |
| dc.title.none.fl_str_mv |
The Lorenz chaotic systems as nonlinear oscillators with memory The Lorenz chaotic systems as nonlinear oscillators with memory |
| title |
The Lorenz chaotic systems as nonlinear oscillators with memory |
| spellingShingle |
The Lorenz chaotic systems as nonlinear oscillators with memory PANCHEV, S. CHAOTIC SYSTEMS MEMORY FUNCTION DUFFING OSCILLATOR Chaotic systems memory function duffing oscillator |
| title_short |
The Lorenz chaotic systems as nonlinear oscillators with memory |
| title_full |
The Lorenz chaotic systems as nonlinear oscillators with memory |
| title_fullStr |
The Lorenz chaotic systems as nonlinear oscillators with memory |
| title_full_unstemmed |
The Lorenz chaotic systems as nonlinear oscillators with memory |
| title_sort |
The Lorenz chaotic systems as nonlinear oscillators with memory |
| dc.creator.none.fl_str_mv |
PANCHEV, S. SPASSOVA, T. |
| author |
PANCHEV, S. |
| author_facet |
PANCHEV, S. SPASSOVA, T. |
| author_role |
author |
| author2 |
SPASSOVA, T. |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
CHAOTIC SYSTEMS MEMORY FUNCTION DUFFING OSCILLATOR Chaotic systems memory function duffing oscillator |
| topic |
CHAOTIC SYSTEMS MEMORY FUNCTION DUFFING OSCILLATOR Chaotic systems memory function duffing oscillator |
| description |
Nonlinear dynamical systems (systems of 1st order ordinary differential equations) capable of generating chaos are analytically nonintegrable. Despite of this fact, analytical tools can be used to extract useful information. In this paper the original Lorenz system and its modifications are reduced to single oscillatory type integral-differential equations with delayed argument. This yields to appearance of an ‘‘endogenous’’ term interpreted as memory for the past. Moreover, the equations are valid far from the initial instant (theoretically at t→∞), when the system eventually evolves on its attractor set. This corresponds to the numerical solutions when an appropriate initial part of the iterates is usually discarded to eliminate the transients. Besides, the form of the equations allows statistical treatment. |
| publishDate |
2009 |
| dc.date.none.fl_str_mv |
2009-10-05 |
| 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://www.revistascca.unam.mx/atm/index.php/atm/article/view/8527 |
| url |
https://www.revistascca.unam.mx/atm/index.php/atm/article/view/8527 |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.none.fl_str_mv |
https://www.revistascca.unam.mx/atm/index.php/atm/article/view/8527/7997 |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.none.fl_str_mv |
Instituto de Ciencias de la Atmósfera y Cambio Climático, Universidad Nacional Autónoma de México |
| publisher.none.fl_str_mv |
Instituto de Ciencias de la Atmósfera y Cambio Climático, Universidad Nacional Autónoma de México |
| dc.source.none.fl_str_mv |
Atmósfera; Vol. 17 Núm. 3 (2004) Atmósfera; Vol. 17 No. 3 (2004) 2395-8812 0187-6236 reponame:Atmósfera instname:UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO instacron:UNAM |
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UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO |
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UNAM |
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UNAM |
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Atmósfera |
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Atmósfera |
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1858175140805738496 |
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15,81155 |