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On the Coexistence of Two Limit Cycles Enclosing a Node in a Class of Planar Differential Systems of Degree Six.

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Τίτλος: On the Coexistence of Two Limit Cycles Enclosing a Node in a Class of Planar Differential Systems of Degree Six.
Συγγραφείς: Khireddine, Fouad1,2 (AUTHOR) fo.khireddine@univ-boumerdes.dz, Grazem, Mohamed1,3 (AUTHOR)
Πηγή: Mathematical Methods in the Applied Sciences. Sep2026, p1. 8p. 2 Illustrations.
Θεματικοί όροι: *Limit cycles, *Mathematical singularities, *Differentiable dynamical systems
Περίληψη: ABSTRACT In this paper, we look at a special type of six‐degree polynomial differential systems in the plane. We establish the coexistence of two limit cycles in these systems, both surrounding a single node. It is well known that, for systems of even degree, proving the coexistence of multiple limit cycles is highly challenging. To the best of our knowledge, this configuration is obtained here for the first time. We provide a rigorous proof of the result and present explicit examples illustrating the occurrence of two nested limit cycles surrounding the same singular point. [ABSTRACT FROM AUTHOR]
Βάση Δεδομένων: Academic Search Index
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  Data: On the Coexistence of Two Limit Cycles Enclosing a Node in a Class of Planar Differential Systems of Degree Six.
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  Data: <searchLink fieldCode="AR" term="%22Khireddine%2C+Fouad%22">Khireddine, Fouad</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> fo.khireddine@univ-boumerdes.dz</i><br /><searchLink fieldCode="AR" term="%22Grazem%2C+Mohamed%22">Grazem, Mohamed</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Mathematical+Methods+in+the+Applied+Sciences%22">Mathematical Methods in the Applied Sciences</searchLink>. Sep2026, p1. 8p. 2 Illustrations.
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  Data: *<searchLink fieldCode="DE" term="%22Limit+cycles%22">Limit cycles</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+singularities%22">Mathematical singularities</searchLink><br />*<searchLink fieldCode="DE" term="%22Differentiable+dynamical+systems%22">Differentiable dynamical systems</searchLink>
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  Data: ABSTRACT In this paper, we look at a special type of six‐degree polynomial differential systems in the plane. We establish the coexistence of two limit cycles in these systems, both surrounding a single node. It is well known that, for systems of even degree, proving the coexistence of multiple limit cycles is highly challenging. To the best of our knowledge, this configuration is obtained here for the first time. We provide a rigorous proof of the result and present explicit examples illustrating the occurrence of two nested limit cycles surrounding the same singular point. [ABSTRACT FROM AUTHOR]
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      – Type: doi
        Value: 10.1002/mma.71009
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 8
        StartPage: 1
    Subjects:
      – SubjectFull: Limit cycles
        Type: general
      – SubjectFull: Mathematical singularities
        Type: general
      – SubjectFull: Differentiable dynamical systems
        Type: general
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      – TitleFull: On the Coexistence of Two Limit Cycles Enclosing a Node in a Class of Planar Differential Systems of Degree Six.
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            NameFull: Khireddine, Fouad
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            NameFull: Grazem, Mohamed
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          Dates:
            – D: 27
              M: 09
              Text: Sep2026
              Type: published
              Y: 2026
          Identifiers:
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            – TitleFull: Mathematical Methods in the Applied Sciences
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