WIAS Preprint No. 2864, (2021)
Global algebraic Poincaré--Bendixson annulus for van der Pol systems
Authors
- Grin, Alexander
- Schneider, Klaus R.
2020 Mathematics Subject Classification
- 34C05 34C07 34C23
Keywords
- Limit cycle, equivalent van der Pol systems, Dulac--Cherkas function, Poincaré--Bendixson annulus, singularly perturbed system
DOI
Abstract
By means of planar polynomial systems topologically equivalent to the van der Pol system we demonstrate an approach to construct algebraic transversal ovals forming a parameter depending Poincaré-Bendixson annulus which contains a unique limit cycle for the full parameter domain. The inner boundary consists of the zero-level set of a special Dulac-Cherkas function which implies the uniqueness of the limit cycle. For the construction of the outer boundary we present a corresponding procedure
Appeared in
- Electron. J. Qual. Theory Differ. Equ., (2023), pp. 1--12, DOI 10.14232/ejqtde.2023.1.35 .
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