WIAS Preprint No. 2638, (2019)

Lower and upper bounds for the number of limit cycles on a cylinder



Authors

  • Schneider, Klaus R.
  • Grin, Alexander

2010 Mathematics Subject Classification

  • 34C05 34C07

Keywords

  • Autonomous systems with cylindrical phase space, location and number of limit cycles of second kind, Dulac--Cherkas function, factorized Dulac function

DOI

10.20347/WIAS.PREPRINT.2638

Abstract

We consider autonomous systems with cylindrical phase space. Lower and upper bounds for the number of limit cycles surrounding the cylinder can be obtained by means of an appropriate Dulac-Cherkas function. We present different possibilities to improve these bounds including the case that the exact number of limit cycles can be determined. These approaches are based on the use of several Dulac-Cherkas functions or on applying some factorized Dulac function.

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