主讲人：Armengol Gasull 教授 

单 位：西班牙巴塞罗那自治大学 

题 目：Stability and bifurcation values for an one-parameter planar system 

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.                      

报告人简介：西班牙巴塞罗那自治大学的A.Gasull教授在常微分方程与动力系统领域是国际知名学者之一，他在连续动力系统、离散动力系统、非光滑或不连续动力系统、差分方程、数学模型、希尔伯特第十六问题等方面的研究都十分活跃，已发表论文130余篇。除了经常应邀在国际会议上报告外，他还多次组织国际会议或国际研讨会。他曾数次应邀来中国访问，进行交流与合作。