Some results on homoclinic and heteroclinic connections in planar systems
Some results on homoclinic and heteroclinic connections in planar systems
复制标题
平面系统中同宿和异宿连接的一些结果
DOI：
10.1088/0951-7715/23/12/001
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发表时间：
2009
期刊：
影响因子：
1.7
通讯作者：
Joan Torregrosa
中科院分区：
文献类型：
--
作者：
A. Gasull;H. Giacomini;Joan Torregrosa
Consider a family of planar systems depending on two parameters (n, b) and having at most one limit cycle. Assume that the limit cycle disappears at some homoclinic (or heteroclinic) connection when Φ(n, b) = 0. We present a method that allows us to obtain a sequence of explicit algebraic lower and upper bounds for the bifurcation set Φ(n, b) = 0. The method is applied to two quadratic families, one of them is the well-known Bogdanov–Takens system. One of the results that we obtain for this system is the bifurcation curve for small values of n, given by . We obtain the new three terms from purely algebraic calculations, without evaluating Melnikov functions.
