Global algebraic Poincaré-Bendixson annulus for the van der Pol system

DOI10.1134/S0012266122030016zbMath1502.34040WikidataQ115248826 ScholiaQ115248826MaRDI QIDQ2671936

Alexander Grin, Klaus R. Schneider

Publication date: 7 June 2022

Published in: Differential Equations (Search for Journal in Brave)

zbMATH Keywords

limit cycleplanar systemautonomous systemPoincaré-Bendixson annulus

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

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Cites Work

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• Upper bounds for the number of limit cycles through linear differential equations
• Transversal conics and the existence of limit cycles
• Qualitative theory of planar differential systems
• Some Applications of the Extended Bendixson-Dulac Theorem
• Dulac-Cherkas functions for generalized Liénard systems
• New approach to study the van der Pol equation for large damping
• EFFECTIVE CONSTRUCTION OF POINCARÉ-BENDIXSON REGIONS