Abstract
New methods for constructing two Dulac–Cherkas functions are developed using which abetter, depending on the parameter \(\lambda >0\) , innerboundary of the Poincaré–Bendixson annulus \(A(\lambda )\) is found for the Rayleigh system. A procedure isproposed for directly finding a polynomial whose zero level set contains a transversal oval used asthe outer boundary of \(A(\lambda )\) . Aninterval for \(\lambda\) is specified with which the best outer boundary ofthe annulus \(A(\lambda )\) is a closed contour composed of twoarcs of the constructed oval and two arcs of unclosed curves of the zero level set of one of theDulac–Cherkas functions. Thus, a refined global Poincaré–Bendixson annulus for thelimit cycle of the Rayleigh system is presented.
