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TitleThe problem of general center-focus and bifurcation of limit cycles for a planar system of nine degrees
Author(s) Claudio Dupre, Yu Liu
TypeArticle in Journal
AbstractOur 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 ( − 1 2 , 0 ) , ( − 1 2 , 1 2 ) , ( − 1 2 , − 1 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. What is worth mentioning is that similar conclusions are hardly seen in published papers up till now and our work is completely new.
KeywordsGeneral equivariant system, General center, General fine focus, General focal values, Limit cycle
URL http://www.sciencedirect.com/science/article/pii/S0377042708001441
JournalJournal of Computational and Applied Mathematics
Pages1043 - 1057
Translation No
Refereed No