STABILITY OF SINGULAR LIMIT CYCLES FOR ABEL EQUATIONS

被引：12

作者：

Luis Bravo, Jose ^{[1
]}

Fernandez, Manuel ^{[1
]}

Gasull, Armengol ^{[2
]}

机构：

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

[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2015年 / 35卷 / 05期

关键词：

Abel equation; closed solution; periodic solution; limit cycle; PERIODIC-SOLUTIONS; NUMBER;

D O I：

10.3934/dcds.2015.35.1873

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain a criterion for determining the stability of singular limit cycles of Abel equations x' = A(t)x(3) + B(t)x(2). This stability controls the possible saddle-node bifurcations of limit cycles. Therefore, studying the Hopf-like bifurcations at x = 0, together with the bifurcations at infinity of a suitable compactification of the equations, we obtain upper bounds of their number of limit cycles. As an illustration of this approach, we prove that the family x(') = at(t - t(A))x(3) + b(t - t(B))x(2), with a,b>0, has at most two positive limit cycles for any t(B), t(A).

引用

页码：1873 / 1890

页数：18

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