Stability and bifurcation values for an one-parameter planar system
讲座名称：
Stability and bifurcation values for an one-parameter planar system
讲座时间：
2013-10-18
讲座人：
Armengol Gasull
形式：
校区：
兴庆校区
实践学分：
讲座内容：
题 目：Stability and bifurcation values for an one-parameter planar system
主讲人：Armengol Gasull 教授
单 位：西班牙巴塞罗那自治大学
时 间：2013年10月18日上午 9:00
地 点：理科楼-408
摘 要：We consider the 1-parameter family of planar quintic systems, x˙ = y^3-x^3, y˙ = -x + my^5, introduced by A. Bacciotti in 1985. It is known that it has at most one limit cycle and that it can exist only when the parameter m is in (0.36; 0.6). In this paper, using the Bendixon-Dulac theorem, we give a new unified proof of all the previous results, we shrink this interval to (0.547; 0.6), and we prove the hyperbolicity of the limit cycle. We also consider the question of the existence of polycycles. The main interest and difficulty for studying this family is that it is not a semi-complete family of rotated vector fields. Finally we answer an open question about the change of stability of the origin for an extension of the above systems.
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