View in EDS HTML Full Text PDF Full Text

Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields.

Saved in:
Bibliographic Details
Title: Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields.
Authors: Cardoso, João L.1 (AUTHOR), Llibre, Jaume2 (AUTHOR), Novaes, Douglas D.3 (AUTHOR), Tonon, Durval J.1 (AUTHOR) djtonon@ufg.br
Source: Dynamical Systems: An International Journal. Sep2020, Vol. 35 Issue 3, p490-514. 25p.
Subjects: Chebyshev systems, Limit cycles, Vector fields, Linear systems, Positive systems, Infinity (Mathematics)
Abstract: In the present study, we consider planar piecewise linear vector fields with two zones separated by the straight line x = 0. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, we provide a canonical form for these systems assuming that each linear system has centre, a real one for y<0 and a virtual one for y>0, and such that the real centre is a global centre. Then, working with a first-order piecewise linear perturbation we obtain piecewise linear differential systems with three crossing limit cycles. Second, we see that a sliding cycle can be detected after a second-order piecewise linear perturbation. Finally, imposing the existence of a sliding limit cycle we prove that only one adittional crossing limit cycle can appear. Furthermore, we also characterize the stability of the higher amplitude limit cycle and of the infinity. The main techniques used in our proofs are the Melnikov method, the Extended Chebyshev systems with positive accuracy, and the Bendixson transformation. [ABSTRACT FROM AUTHOR]
Copyright of Dynamical Systems: An International Journal is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
Full text is not displayed to guests.
FullText Links:
  – Type: pdflink
Text:
  Availability: 1
Header DbId: egs
DbLabel: Engineering Source
An: 145732479
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields.
– Name: Author
  Label: Authors
  Group: Au
  Data: &lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Cardoso%2C+Jo&#227;o+L%2E%22&quot;&gt;Cardoso, Jo&#227;o L.&lt;/searchLink&gt;&lt;relatesTo&gt;1&lt;/relatesTo&gt; (AUTHOR)&lt;br /&gt;&lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Llibre%2C+Jaume%22&quot;&gt;Llibre, Jaume&lt;/searchLink&gt;&lt;relatesTo&gt;2&lt;/relatesTo&gt; (AUTHOR)&lt;br /&gt;&lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Novaes%2C+Douglas+D%2E%22&quot;&gt;Novaes, Douglas D.&lt;/searchLink&gt;&lt;relatesTo&gt;3&lt;/relatesTo&gt; (AUTHOR)&lt;br /&gt;&lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Tonon%2C+Durval+J%2E%22&quot;&gt;Tonon, Durval J.&lt;/searchLink&gt;&lt;relatesTo&gt;1&lt;/relatesTo&gt; (AUTHOR)&lt;i&gt; djtonon@ufg.br&lt;/i&gt;
– Name: TitleSource
  Label: Source
  Group: Src
  Data: &lt;searchLink fieldCode=&quot;JN&quot; term=&quot;%22Dynamical+Systems%3A+An+International+Journal%22&quot;&gt;Dynamical Systems: An International Journal&lt;/searchLink&gt;. Sep2020, Vol. 35 Issue 3, p490-514. 25p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: &lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Chebyshev+systems%22&quot;&gt;Chebyshev systems&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Limit+cycles%22&quot;&gt;Limit cycles&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Vector+fields%22&quot;&gt;Vector fields&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Linear+systems%22&quot;&gt;Linear systems&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Positive+systems%22&quot;&gt;Positive systems&lt;/searchLink&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;DE&quot; term=&quot;%22Infinity+%28Mathematics%29%22&quot;&gt;Infinity (Mathematics)&lt;/searchLink&gt;
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In the present study, we consider planar piecewise linear vector fields with two zones separated by the straight line x = 0. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, we provide a canonical form for these systems assuming that each linear system has centre, a real one for y&lt;0 and a virtual one for y&gt;0, and such that the real centre is a global centre. Then, working with a first-order piecewise linear perturbation we obtain piecewise linear differential systems with three crossing limit cycles. Second, we see that a sliding cycle can be detected after a second-order piecewise linear perturbation. Finally, imposing the existence of a sliding limit cycle we prove that only one adittional crossing limit cycle can appear. Furthermore, we also characterize the stability of the higher amplitude limit cycle and of the infinity. The main techniques used in our proofs are the Melnikov method, the Extended Chebyshev systems with positive accuracy, and the Bendixson transformation. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: &lt;i&gt;Copyright of Dynamical Systems: An International Journal is the property of Taylor &amp; Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder&#39;s express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.&lt;/i&gt; (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=145732479
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1080/14689367.2020.1722064
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 25
        StartPage: 490
    Subjects:
      – SubjectFull: Chebyshev systems
        Type: general
      – SubjectFull: Limit cycles
        Type: general
      – SubjectFull: Vector fields
        Type: general
      – SubjectFull: Linear systems
        Type: general
      – SubjectFull: Positive systems
        Type: general
      – SubjectFull: Infinity (Mathematics)
        Type: general
    Titles:
      – TitleFull: Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Cardoso, João L.
      – PersonEntity:
          Name:
            NameFull: Llibre, Jaume
      – PersonEntity:
          Name:
            NameFull: Novaes, Douglas D.
      – PersonEntity:
          Name:
            NameFull: Tonon, Durval J.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 09
              Text: Sep2020
              Type: published
              Y: 2020
          Identifiers:
            – Type: issn-print
              Value: 14689367
          Numbering:
            – Type: volume
              Value: 35
            – Type: issue
              Value: 3
          Titles:
            – TitleFull: Dynamical Systems: An International Journal
              Type: main
ResultId 1