On the number of limit cycles in piecewise smooth generalized Abel equations with two asymmetric zones

讲座时间 Datetime: 2022年9月7日，星期三，16:30-17:30

地点 Venue: 腾讯会议：432-952-975

主持人 Host：彭亚群

报告人 Speaker: 黄健沨  

单位 Affiliation: 暨南大学

报告摘要 Abstract:

This paper devotes to the study of a kind of generalized Abel equation, where the coefficients are piecewise trigonometrical polynomials of degree m with two zones separated by a vertical straight line. We focus on the maximum number of positive and negative limit cycles (i.e., positive and negative isolated periodic solutions) that the equation can have, and the problem that how this maximum number, denoted by H(m), is affected by the location of the separation line. Then, by virtue of arbitrary higher order analysis using the theories of Melnikov functions and Chebyshev systems, we characterize the lower bounds for H(m). This result includes the estimates for not only the classical Abel equations but also some other equations from the real problems, such as the pendulum-like equations. In general, the asymmetry of the two zones increases the number of limit cycles in comparison with the case where the two zones are symmetric.