In this paper, we study a class of quasi-symmetric seventh degree system. By making two appropriate transformations of system (3) and calculating general focal values carefully, we obtain the conditions that the infinity and the elementary focus (-1 2 , 0) become centers at the same time. Moreover,
The problem of general center-focus and bifurcation of limit cycles for a planar system of nine degrees
โ Scribed by Chaoxiong Du; Yirong Liu
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 1023 KB
- Volume
- 223
- Category
- Article
- ISSN
- 0377-0427
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โฆ Synopsis
Our researches are concerned with a class of planar general equivariant system of nine degrees. By making two appropriate transformations of system and calculating focal values carefully, we obtain the conditions that the infinity and three elementary focuses
2 ) become four general centers at the same time. Moreover, 20 limit cycles including 15 small limit cycles from three elementary foci and 5 large limit cycles from the infinity can occur under a certain condition.
๐ SIMILAR VOLUMES
In this paper, center conditions and bifurcation of limit cycles from the equator for a class of polynomial system of degree seven are studied. The method is based on converting a real system into a complex system. The recursion formula for the computation of singular point quantities of complex sys