On a Dulac function for the Kukles system
type: Item
instance of: scholarly article
title: On a Dulac function for the Kukles system
zbMATH Open document ID: 1285.34019
DOI: 10.1134/S0012266110060066
author: Alexander Grin
author: Leonid Cherkas
published in: Differential Equations
publication date: 2010-12-08T00:00:00Z
review text: Consider the planar system \[ \dot x=y,\;\dot y= h_0(x)+ h_1(x)y+ h_2(x) y^2+ h_3(x) y^3,\tag{\(*\)} \] where the functions \(h_i\) are sufficiently smooth and \(h_0(0)= 0\). The goal of the authors is to estimate the number of limit cycles of system \((*)\) and their location by means of a generalized Dulac function. The authors describe an analytic way (based on solving linear differential equations) and a numerical approach (based on solving linear programming problems) to construct such functions in some strip of the phase plane. The proposed methods are applied to some examples.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 5824133
zbMATH Keywords: number of limit cycles
MaRDI profile type: Publication
cites work: Mathematical problems for the next century
cites work: Centennial History of Hilbert's 16th Problem
cites work: Q2706801
cites work: Q5442023
cites work: Dulac functions for Lienard systems
cites work: Spline approximations in the problem of estimating the number of limit cycles of autonomous systems on the plane
cites work: Reduction to transversality of curves in the construction of a Dulac function
cites work: Upper bounds for the number of limit cycles through linear differential equations
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description: scientific article; zbMATH DE number 5824133