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A Refined Global Poincaré–Bendixson Annuluswith the Limit Cycle of the Rayleigh System
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A Refined Global Poincaré–Bendixson Annuluswith the Limit Cycle of the Rayleigh System
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Journal Article
A Refined Global Poincaré–Bendixson Annuluswith the Limit Cycle of the Rayleigh System
2024
Overview
New methods for constructing two Dulac–Cherkas functions are developed using which a better, depending on the parameter , inner boundary of the Poincaré–Bendixson annulus is found for the Rayleigh system. A procedure is proposed for directly finding a polynomial whose zero level set contains a transversal oval used as the outer boundary of . An interval for is specified with which the best outer boundary of the annulus is a closed contour composed of two arcs of the constructed oval and two arcs of unclosed curves of the zero level set of one of the Dulac–Cherkas functions. Thus, a refined global Poincaré–Bendixson annulus for the limit cycle of the Rayleigh system is presented.
Publisher
Springer Nature B.V
Subject
