Publicação
Robust non-computability of dynamical systems and computability of robust dynamical systems
| datacite.subject.sdg | 09:Indústria, Inovação e Infraestruturas | |
| datacite.subject.sdg | 04:Educação de Qualidade | |
| datacite.subject.sdg | 08:Trabalho Digno e Crescimento Económico | |
| dc.contributor.author | Graça, Daniel | |
| dc.contributor.author | Zhong, Ning | |
| dc.date.accessioned | 2026-05-11T15:22:50Z | |
| dc.date.available | 2026-05-11T15:22:50Z | |
| dc.date.issued | 2024-06-26 | |
| dc.description.abstract | In this paper, we examine the relationship between the stability of the dynamical system x ′ = f(x) and the computability of its basins of attraction. We present a computable C ∞ system x ′ = f(x) that possesses a computable and stable equilibrium point, yet whose basin of attraction is robustly non-computable in a neighborhood of f in the sense that both the equilibrium point and the non-computability of its associated basin of attraction persist when f is slightly perturbed. This indicates that local stability near a stable equilibrium point alone is insufficient to guarantee the computability of its basin of attraction. However, we also demonstrate that the basins of attraction associated with a structurally stable - globally stable (robust) - planar system defined on a compact set are computable. Our findings suggest that the global stability of a system and the compactness of the domain play a pivotal role in determining the computability of its basins of attraction. | eng |
| dc.identifier.doi | 10.46298/lmcs-20(2:19)2024 | |
| dc.identifier.issn | 1860-5974 | |
| dc.identifier.uri | http://hdl.handle.net/10400.1/28921 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | Centre pour la Communication Scientifique Directe (CCSD) | |
| dc.relation | Instituto de Telecomunicações | |
| dc.relation | Computing with Infinite Data | |
| dc.relation.ispartof | Logical Methods in Computer Science | |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Non-computability | |
| dc.subject | Basin of attraction | |
| dc.subject | Dynamical systems | |
| dc.subject | Ordinary differential equations | |
| dc.subject | Structural stability | |
| dc.title | Robust non-computability of dynamical systems and computability of robust dynamical systems | eng |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardNumber | UIDB/50008/2020 | |
| oaire.awardNumber | 731143 | |
| oaire.awardTitle | Instituto de Telecomunicações | |
| oaire.awardTitle | Computing with Infinite Data | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F50008%2F2020/PT | |
| oaire.awardURI | info:eu-repo/grantAgreement/EC/H2020/731143/EU | |
| oaire.citation.issue | 2 | |
| oaire.citation.title | Logical Methods in Computer Science | |
| oaire.citation.volume | Volume 20 | |
| oaire.fundingStream | 6817 - DCRRNI ID | |
| oaire.fundingStream | H2020 | |
| oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |
| person.familyName | Graça | |
| person.givenName | Daniel | |
| person.identifier.ciencia-id | 2D11-56DE-3F11 | |
| person.identifier.orcid | 0000-0002-0330-833X | |
| person.identifier.rid | D-2335-2011 | |
| person.identifier.scopus-author-id | 8882791800 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.identifier | http://doi.org/10.13039/501100008530 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| project.funder.name | European Commission | |
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