学术报告预告(主讲人:Jaume Llibre,时间:10月14日)

作者: 时间:2024-10-12 点击数:

学术报告预告(主讲人:Jaume Llibre,时间:10月14日)

报告题目:HOPF BIFURCATION OF LIMIT CYCLES SURROUNDING A NODE

报告人:Jaume Llibre 西班牙皇家科学院院士

报告邀请人:梁海华

报告时间:2024年10月14日(星期一),10:00-11:30

报告地点:学校东校区广东工业实训中心803室(校友办活动室)

内容摘要:We consider the planar polynomial differential systems in R2 x˙ = μx + P(x, y, μ), y˙ = μy + Q(x, y, μ),where the polynomials P and Q have neither constant terms nor linear terms, satisfying that when the parameter |μ| ̸= 0 and small, the origin is a node, and for μ = 0 the origin is either a node or a focus.The main theorem characterizes the Hopf bifurcation from the equilibrium point at the origin of this system.We illustrate this result with several examples.As a consequence, we can give a lower bound for the number of small limit cycles surrounding a node depending only on the degree of the polynomial differential system.In summary, we extend the Hopf bifurcation that usually studies the bifurcation of limit cycles from a focus to the bifurcation of limit cycles from a node.

In this talk the node at the origin is an star node, but the results that I will present for the star node also work for the standard node ˙x = μx, y˙ = λy with μλ > 0, or for the non-diagonalizable node ˙x = μx + y, y˙ = μy.

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