學(xué)術(shù)報(bào)告預(yù)告（主講人：Jaume Llibre，時(shí)間：10月14日）
報(bào)告題目：HOPF BIFURCATION OF LIMIT CYCLES SURROUNDING A NODE
報(bào)告人：Jaume Llibre 西班牙皇家科學(xué)院院士
報(bào)告邀請(qǐng)人：梁海華
報(bào)告時(shí)間：2024年10月14日（星期一），10：00-11：30
報(bào)告地點(diǎn)：學(xué)校東校區(qū)廣東工業(yè)實(shí)訓(xùn)中心803室（校友辦活動(dòng)室）
內(nèi)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.
歡迎感興趣的老師和同學(xué)參加，請(qǐng)至少提前15分鐘到場(chǎng)！
美獅貴賓官方網(wǎng)站
