Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	黄博，北京航空航天大学
Inviter:
Title:	On the Number of Limit Cycles from Zero-Hopf Bifurcation for Certain Differential Systems
Time & Venue:	2022.05.18 10:30-11:30 南楼N913 腾讯会议：532-920-864 密码：0518
Abstract:	In this talk, I will introduce some new results on the number of limit cycles from zero-Hopf bifurcation for certain differential systems. The system in question is assumed to be of dimension $n$, have a zero-Hopf equilibrium at the origin, and consist only of homogeneous terms of order $m$. Using the averaging method, we obtain some upper bounds for the number of limit cycles for generic $n\geq3$ and $m\geq2$. The exact numbers of limit cycles or tight bounds on the numbers are determined by computing the mixed volumes of some polynomial systems obtained from the averaged functions. Based on symbolic computation, a general and algorithmic approach is proposed to derive sufficient conditions for a given differential system to have a prescribed number of limit cycles. The effectiveness of the proposed approach is illustrated by a family of third-order differential equations and by a four-dimensional hyperchaotic differential system. This is based on my joint work with Prof. Dongming Wang.