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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数学与系统科学学院
