Limit cycles of the Higgins–Selkov system and the Selkov system

讲座时间 Datetime: 2022年5月21日，星期六，15:30-16:30

地点 Venue: 腾讯线上会议：370-526-311

 主持人 Host：刘长剑

报告人 Speaker:陈和柏

单位 Affiliation:中南大学

报告摘要 Abstract:

In this talk, we introduce a proof of Artés–Llibre–Valls’s conjectures on the uniqueness of limit cycles for the Higgins–Selkov system and the Selkov system. In order to apply the limit cycle theory for Liénard systems, we change the Higgins–Selkov and the Selkov systems into Liénard systems first. Then, we present two theorems on the nonexistence of limit cycles of Liénard systems and one theorem on the uniqueness of limit cycles for a general Liénard system, which allows for discontinuity. At last, the conjectures can be proven by these theorems and some techniques applied for Liénard systems.