Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center
From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles tha...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:199322 |
| Acceso en línea: | https://ddd.uab.cat/record/199322 https://dx.doi.org/urn:doi:10.1016/j.jmaa.2018.07.024 |
| Access Level: | acceso abierto |
| Palabra clave: | Discontinuous piecewise linear differential system Limit cycle Non-smooth differential system |
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ES_f535b10affc19ac1466835666938adde |
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oai:ddd.uab.cat:199322 |
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ES |
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España |
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Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center Llibre, Jaume|||0000-0002-9511-5999 Zhang, Xiang|||0000-0001-5194-4077 Discontinuous piecewise linear differential system Limit cycle Non-smooth differential system From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles that this class of differential systems can have? Here we prove that when one of the linear differential systems has a center, real or virtual, then the discontinuous piecewise linear differential system has at most two limit cycles. https://ddd.uab.cat/record/199322 https://dx.doi.org/urn:doi:10.1016/j.jmaa.2018.07.024 |
| title |
Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center |
| spellingShingle |
Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center Llibre, Jaume|||0000-0002-9511-5999 Discontinuous piecewise linear differential system Limit cycle Non-smooth differential system |
| title_short |
Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center |
| title_full |
Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center |
| title_fullStr |
Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center |
| title_full_unstemmed |
Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center |
| title_sort |
Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center |
| author |
Llibre, Jaume|||0000-0002-9511-5999 |
| author_facet |
Llibre, Jaume|||0000-0002-9511-5999 Zhang, Xiang|||0000-0001-5194-4077 |
| author_role |
author |
| author2 |
Zhang, Xiang|||0000-0001-5194-4077 |
| author2_role |
author |
| topic |
Discontinuous piecewise linear differential system Limit cycle Non-smooth differential system |
| topic_facet |
Discontinuous piecewise linear differential system Limit cycle Non-smooth differential system |
| description |
From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles that this class of differential systems can have? Here we prove that when one of the linear differential systems has a center, real or virtual, then the discontinuous piecewise linear differential system has at most two limit cycles. |
| publishDate |
2018 |
| format |
article |
| url |
https://ddd.uab.cat/record/199322 https://dx.doi.org/urn:doi:10.1016/j.jmaa.2018.07.024 |
| language |
eng |
| eu_rights_str_mv |
openAccess |
| institution |
Universitat Autònoma de Barcelona |
| collection |
Dipòsit Digital de Documents de la UAB |
| reponame_str |
Dipòsit Digital de Documents de la UAB |
| instname_str |
Universitat Autònoma de Barcelona |
| _version_ |
1878443002470334464 |
| publishDateSort |
2018 |
| author_browse |
Llibre, Jaume|||0000-0002-9511-5999 Zhang, Xiang|||0000-0001-5194-4077 |
| score |
6.924472 |