第三讲 平面奇点指数

1、2020/7/19,1,第三讲 平面奇点指数,连续向量场的旋转数 平面奇点指标 平面系统以及二维非自治连续系统 的局部分岔与全局分岔 中心流形,2020/7/19,2,2020/7/19,3,连续向量场的旋转数,2020/7/19,4,2020/7/19,5,2020/7/19,6,旋转数定义,2020/7/19,7,旋转数计算公式,2020/7/19,8,2020/7/19,9,2020/7/19,10,2020/7/19,11,2020/7/19,12,2020/7/19,13,2020/7/19,14,2020/7/19,15,平面奇点指数,2020/7/19,16,2020/7/19,

2、17,2020/7/19,18,2020/7/19,19,2020/7/19,20,2020/7/19,21,2020/7/19,22,2020/7/19,23,2020/7/19,24,2020/7/19,25,2020/7/19,26,2020/7/19,27,2020/7/19,28,2020/7/19,29,2020/7/19,30,2020/7/19,31,性质,2020/7/19,32,推论,2020/7/19,33,平面系统以及二维非自治连续系统 的局部分岔与全局分岔,向量场不动点的分岔 具有一个零特征根 Saddle-node bifurcation Transcritical

3、 bifurcation Pitchfork bifurcation 一对纯虚根：Hopf分岔,2020/7/19,34,向量场不动点的分岔,2020/7/19,35,具有一个零特征根,2020/7/19,36,2020/7/19,37,Transcritical bifurcation,2020/7/19,38,2020/7/19,39,Pitchfork bifurcation,2020/7/19,40,2020/7/19,41,一对纯虚根：Hopf分岔,2020/7/19,42,2020/7/19,43,2020/7/19,44,2020/7/19,45,2020/7/19,46,d0,

4、a0,supercritical bifurcation,2020/7/19,47,2020/7/19,48,2020/7/19,49,中心流形(center manifold),2020/7/19,50,2020/7/19,51,2020/7/19,52,2020/7/19,53,2020/7/19,54,2020/7/19,55,2020/7/19,56,2020/7/19,57,2020/7/19,58,2020/7/19,59,2020/7/19,60,2020/7/19,61,2020/7/19,62,2020/7/19,63,2020/7/19,64,2020/7/19,65,2020/7/19,66,极限点,2020/7/19,67,极限集,2020/7/19,68,吸引集,2020/7/19,69,吸引盆,2020/7/19,70,吸引子,2020/7/19,71,极限集性质,2020/7/19,72,Poincar-Bendixson定理