Global Algebraic Poincaré–Bendixson Annulus for the van der Pol System View Full Text


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Article Info

DATE

2022-03

AUTHORS

А. А. Grin, К. R. Schneider

ABSTRACT

We construct analytically two algebraic closed curves forming a Poincaré–Bendixson annulus for the van der Pol system for all values of its parameter. The inner boundary of the annulus is a closed curve of the zero-level set of a Dulac–Cherkas function, which implies that this annulus contains at most one limit cycle. For the construction of the outer boundary a special procedure is presented. More... »

PAGES

285-295

References to SciGraph publications

  • 2001. Differential Equations and Dynamical Systems in NONE
  • 2013-07-11. Some Applications of the Extended Bendixson-Dulac Theorem in PROGRESS AND CHALLENGES IN DYNAMICAL SYSTEMS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1134/s0012266122030016

    DOI

    http://dx.doi.org/10.1134/s0012266122030016

    DIMENSIONS

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