Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations
The global attractor of a skew product semiflow for a non-autonomous differential equation describes the asymptotic behaviour of the model. This attractor is usually characterized as the union, for all the parameters in the base space, of the associated cocycle attractors in the product space. The c...
| Authors: | ; ; |
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| Format: | Article |
| Status: | Submitted version |
| Publication date: | 2017 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/58657 |
| Online Access: | http://hdl.handle.net/11441/58657 https://doi.org/10.1088/1361-6544/30/1/274 |
| Access Level: | Open access |
| Keyword: | Global attractor Pullback attractor Forward attractor 1D non-autonomous linear differential equation Chaotic behavior in Li-Yorke sense Chaotic behavior in Auslander-Yorke sense |
| _version_ | 1878742435797925888 |
|---|---|
| author | Caraballo Garrido, Tomás |
| author2 | Langa Rosado, José Antonio Obaya García, Rafael |
| author2_role | author author |
| author_browse | Caraballo Garrido, Tomás Langa Rosado, José Antonio Obaya García, Rafael |
| author_facet | Caraballo Garrido, Tomás Langa Rosado, José Antonio Obaya García, Rafael |
| author_role | author |
| collection | idUS. Depósito de Investigación de la Universidad de Sevilla |
| description | The global attractor of a skew product semiflow for a non-autonomous differential equation describes the asymptotic behaviour of the model. This attractor is usually characterized as the union, for all the parameters in the base space, of the associated cocycle attractors in the product space. The continuity of the cocycle attractor in the parameter is usually a difficult question. In this paper we develop in detail a 1D non-autonomous linear differential equation and show the richness of non-autonomous dynamics by focusing on the continuity, characterization and chaotic dynamics of the cocycle attractors. In particular, we analyse the sets of continuity and discontinuity for the parameter of the attractors, and relate them with the eventually forward behaviour of the processes. We will also find chaotic behaviour on the attractors in the Li-Yorke and Auslander-Yorke senses. Note that they hold for linear 1D equations, which shows a crucial difference with respect to the presence of chaotic dynamics in autonomous systems. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_f5e35f44dfd030dc17c33020e20351df |
| institution | Universidad de Sevilla (US) |
| instname_str | Universidad de Sevilla (US) |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:idus.us.es:11441/58657 |
| publishDate | 2017 |
| publishDateSort | 2017 |
| publisher | IOP Publishing |
| publisherStr | IOP Publishing |
| reponame_str | idUS. Depósito de Investigación de la Universidad de Sevilla |
| spelling | Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations Caraballo Garrido, Tomás Langa Rosado, José Antonio Obaya García, Rafael Global attractor Pullback attractor Forward attractor 1D non-autonomous linear differential equation Chaotic behavior in Li-Yorke sense Chaotic behavior in Auslander-Yorke sense The global attractor of a skew product semiflow for a non-autonomous differential equation describes the asymptotic behaviour of the model. This attractor is usually characterized as the union, for all the parameters in the base space, of the associated cocycle attractors in the product space. The continuity of the cocycle attractor in the parameter is usually a difficult question. In this paper we develop in detail a 1D non-autonomous linear differential equation and show the richness of non-autonomous dynamics by focusing on the continuity, characterization and chaotic dynamics of the cocycle attractors. In particular, we analyse the sets of continuity and discontinuity for the parameter of the attractors, and relate them with the eventually forward behaviour of the processes. We will also find chaotic behaviour on the attractors in the Li-Yorke and Auslander-Yorke senses. Note that they hold for linear 1D equations, which shows a crucial difference with respect to the presence of chaotic dynamics in autonomous systems. Fondo Europeo de Desarrollo Regional Ministerio de Economía y Competitividad Junta de Andalucía Brazilian-European partnership in Dynamical Systems (BREUDS) Junta de Castilla y León IOP Publishing http://hdl.handle.net/11441/58657 https://doi.org/10.1088/1361-6544/30/1/274 |
| spellingShingle | Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations Caraballo Garrido, Tomás Global attractor Pullback attractor Forward attractor 1D non-autonomous linear differential equation Chaotic behavior in Li-Yorke sense Chaotic behavior in Auslander-Yorke sense |
| status_str | submittedVersion |
| title | Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations |
| title_full | Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations |
| title_fullStr | Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations |
| title_full_unstemmed | Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations |
| title_short | Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations |
| title_sort | Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations |
| topic | Global attractor Pullback attractor Forward attractor 1D non-autonomous linear differential equation Chaotic behavior in Li-Yorke sense Chaotic behavior in Auslander-Yorke sense |
| topic_facet | Global attractor Pullback attractor Forward attractor 1D non-autonomous linear differential equation Chaotic behavior in Li-Yorke sense Chaotic behavior in Auslander-Yorke sense |
| url | http://hdl.handle.net/11441/58657 https://doi.org/10.1088/1361-6544/30/1/274 |