Spline approximations in the problem of estimating the number of limit cycles of autonomous systems on the plane

DOI10.1134/S0012266106020091zbMath1135.34026MaRDI QIDQ2461863

Alexander Grin, Leonid Cherkas

Publication date: 21 November 2007

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

zbMATH Keywords

Liénard systemlimit cyclesspline interpolationMathematicapredator-prey systemplanelinear programming problemsAutonomous systemsvan der Pol systemDulac operatorHilbert's \(16\)-th problem

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (4)

On a Dulac function for the Kukles system ⋮ Limit cycle function of the second kind for autonomous systems on the cylinder ⋮ Dulac-Cherkas function in a neighborhood of a structurally unstable focus of an autonomous polynomial system on the plane ⋮ Bendixson-Dulac criterion and reduction to global uniqueness in the problem of estimating the number of limit cycles

Uses Software

• Mathematica

Cites Work

• Mathematical problems for the next century
• An effective method of counting the number of limit cycles
• Centennial History of Hilbert's 16th Problem
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