UNIQUENESS OF LIMIT CYCLES FOR QUADRATIC VECTOR FIELDS

被引：2

作者：

Luis Bravo, Jose ^{[1
]}

Fernandez, Manuel ^{[1
]}

Ojeda, Ignacio ^{[1
]}

Sanchez, Fernando ^{[1
]}

机构：

[1] Univ Extremadura, Dept Matemat, Badajoz 06006, Spain

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2019年 / 39卷 / 01期

关键词：

Abel equation; closed solution; periodic solution; limit cycle; algebraic variety; ABEL EQUATIONS; PERIODIC-SOLUTIONS; DIFFERENTIAL-EQUATIONS; 2-DIMENSIONAL SYSTEMS; NUMBER;

D O I：

10.3934/dcds.2019020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article deals with the study of the number of limit cycles surrounding a critical point of a quadratic planar vector field, which, in normal form, can be written as x' = a(1)x - y - a(3)x(2 )+ (2a(2 )+ a(5))xy + a6y(2), y' = x+a(1)y+a(2)x(2) +(2a(3)+a(4))xy-a(2)y(2). In particular, we study the semi-varieties defined in terms of the parameters a(1), a(2),..., a(6) where some classical criteria for the associated Abel equation apply. The proofs will combine classical ideas with tools from computational algebraic geometry.

引用

页码：483 / 502

页数：20

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