Publikation:

Limit cycles as stationary states of an extended harmonic balance ansatz

Lade...
Vorschaubild

Dateien

delPino_2-o15k8zon0c930.pdf
delPino_2-o15k8zon0c930.pdfGröße: 1.66 MBDownloads: 26

Datum

2024

Herausgeber:innen

Kontakt

ISSN der Zeitschrift

Electronic ISSN

ISBN

Bibliografische Daten

Verlag

Schriftenreihe

Auflagebezeichnung

ArXiv-ID

Internationale Patentnummer

Link zur Lizenz

Angaben zur Forschungsförderung

Swiss National Science Foundation: CRSII5 177198/1
Swiss National Science Foundation: CRSII5_206008/1
Deutsche Forschungsgemeinschaft (DFG): 449653034
Deutsche Forschungsgemeinschaft (DFG): SFB1432

Projekt

Open Access-Veröffentlichung
Open Access Gold
Core Facility der Universität Konstanz

Gesperrt bis

Titel in einer weiteren Sprache

Publikationstyp
Zeitschriftenartikel
Publikationsstatus
Published

Erschienen in

Physical Review Research. American Physical Society (APS). 2024, 6(3), 033180. eISSN 2643-1564. Verfügbar unter: doi: 10.1103/physrevresearch.6.033180

Zusammenfassung

A limit cycle is a self-sustained, periodic, isolated motion appearing in autonomous differential equations. As the period of a limit cycle is a priori unknown, finding it as a stationary state of a rotating ansatz is challenging. Correspondingly, its study commonly relies on numerical methodologies (e.g., brute-force time evolution, and variational shooting methods) or circumstantial evidence such as instabilities of fixed points. Alas, such approaches are (i) unable to find all solutions, as they rely on specific initial conditions, and (ii) do not provide analytical intuition about the physical origin of the limit cycles. Here, we (I) develop a multifrequency rotating ansatz with which we (II) find all limit cycles as stationary-state solutions via a semianalytical homotopy continuation. We demonstrate our approach and its performance on the Van der Pol oscillator. Moving beyond this simple example, we show that our method captures all coexisting fixed-point attractors and limit cycles in a modified nonlinear Van der Pol oscillator. Our results facilitate the systematic mapping of out-of-equilibrium phase diagrams, with implications across multiple fields of the natural sciences.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
530 Physik

Schlagwörter

Konferenz

Rezension
undefined / . - undefined, undefined

Forschungsvorhaben

Organisationseinheiten

Zeitschriftenheft

Zugehörige Datensätze in KOPS

Zitieren

ISO 690DEL PINO, Javier, Jan KOSATA, Oded ZILBERBERG, 2024. Limit cycles as stationary states of an extended harmonic balance ansatz. In: Physical Review Research. American Physical Society (APS). 2024, 6(3), 033180. eISSN 2643-1564. Verfügbar unter: doi: 10.1103/physrevresearch.6.033180
BibTex
@article{delPino2024-08-19Limit-70744,
  year={2024},
  doi={10.1103/physrevresearch.6.033180},
  title={Limit cycles as stationary states of an extended harmonic balance ansatz},
  number={3},
  volume={6},
  journal={Physical Review Research},
  author={del Pino, Javier and Kosata, Jan and Zilberberg, Oded},
  note={Article Number: 033180}
}
RDF
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/70744">
    <dc:creator>del Pino, Javier</dc:creator>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/41"/>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/41"/>
    <dcterms:abstract>A limit cycle is a self-sustained, periodic, isolated motion appearing in autonomous differential equations. As the period of a limit cycle is a priori unknown, finding it as a stationary state of a rotating ansatz is challenging. Correspondingly, its study commonly relies on numerical methodologies (e.g., brute-force time evolution, and variational shooting methods) or circumstantial evidence such as instabilities of fixed points. Alas, such approaches are (i) unable to find all solutions, as they rely on specific initial conditions, and (ii) do not provide analytical intuition about the physical origin of the limit cycles. Here, we (I) develop a multifrequency rotating ansatz with which we (II) find all limit cycles as stationary-state solutions via a semianalytical homotopy continuation. We demonstrate our approach and its performance on the Van der Pol oscillator. Moving beyond this simple example, we show that our method captures all coexisting fixed-point attractors and limit cycles in a modified nonlinear Van der Pol oscillator. Our results facilitate the systematic mapping of out-of-equilibrium phase diagrams, with implications across multiple fields of the natural sciences.</dcterms:abstract>
    <dcterms:title>Limit cycles as stationary states of an extended harmonic balance ansatz</dcterms:title>
    <dc:creator>Zilberberg, Oded</dc:creator>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dc:rights>Attribution 4.0 International</dc:rights>
    <dcterms:rights rdf:resource="http://creativecommons.org/licenses/by/4.0/"/>
    <dc:creator>Kosata, Jan</dc:creator>
    <dc:language>eng</dc:language>
    <dcterms:issued>2024-08-19</dcterms:issued>
    <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/70744/1/delPino_2-o15k8zon0c930.pdf"/>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2024-09-06T07:09:39Z</dcterms:available>
    <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/70744"/>
    <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/70744/1/delPino_2-o15k8zon0c930.pdf"/>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:contributor>Kosata, Jan</dc:contributor>
    <dc:contributor>del Pino, Javier</dc:contributor>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2024-09-06T07:09:39Z</dc:date>
    <dc:contributor>Zilberberg, Oded</dc:contributor>
  </rdf:Description>
</rdf:RDF>

Interner Vermerk

xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter

Kontakt
URL der Originalveröffentl.

Prüfdatum der URL

Prüfungsdatum der Dissertation

Finanzierungsart

Kommentar zur Publikation

Allianzlizenz
Corresponding Authors der Uni Konstanz vorhanden
Internationale Co-Autor:innen
Universitätsbibliographie
Ja
Begutachtet
Ja
Diese Publikation teilen