Limit cycles for a variant of a generalized Riccati equation

作者：Llibre Jaume^*; Valls Claudia

来源：Applied Mathematics Letters, 2017, 68: 76-79.

DOI：10.1016/j.aml.2016.11.016

• Generalized Riccati system
• Limit cycles
• Weak 16th Hilbert problem
• Abelian integral

In this paper we provide a lower bound for the maximum number of limit cycles surrounding the origin of systems ((x) over dot, (y) over dot = (x) double over dot) given by a variant of the generalized Riccati equation
(x) double over dot+epsilon x(2n+1) (x) over dot+bx(4n+3) = 0,
where b > 0, b is an element of R, n is a non -negative integer and e is a small parameter. The tool for proving this result uses Abelian integrals.

• 出版日期2017-6