Bendixson-Dulac criterion and reduction to global uniqueness in the problem of estimating the number of limit cycles

DOI10.1134/S0012266110010076zbMath1210.34043OpenAlexW2007604904MaRDI QIDQ981739

Leonid Cherkas, Alexander Grin

Publication date: 2 July 2010

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

Full work available at URL: https://doi.org/10.1134/s0012266110010076

zbMATH Keywords

localization of limit cycles

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (5)

Dulac-Cherkas criterion for exact estimation of the number of limit cycles of autonomous systems on a plane ⋮ Estimate of the number of limit cycles of a second-order autonomous system and their localization ⋮ Dulac-Cherkas function in a neighborhood of a structurally unstable focus of an autonomous polynomial system on the plane ⋮ Stability Analysis of a New E-rumor Model ⋮ A Bendixon–Dulac theorem for some piecewise systems

Cites Work

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• Mathematical problems for the next century
• Reduction to transversality of curves in the construction of a Dulac function
• Spline approximations in the problem of estimating the number of limit cycles of autonomous systems on the plane
• Extrema of the Andronov-Hopf function of a polynomial Lienard system
• On the approximation of the limit cycles function
• Centennial History of Hilbert's 16th Problem

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