General center conditions and bifurcation of limit cycles for a quasi-symmetric seventh degree system

✍ Scribed by Chaoxiong Du; Yirong Liu

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 770 KB
• Volume: 56
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2008.07.022

✦ Synopsis

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, 12 limit cycles including 6 small limit cycles from the elementary focus and 6 large limit cycles from the infinity can occur under a certain condition. What is worth mentioning is that similar conclusions are less and our work is new in terms of research about quasi-symmetric systems up till now.