Fenichel Theory – a coordinate independent framework
时间  Datetime
2023-11-24 10:00 — 11:00
地点  Venue
Zoom APP()
报告人  Speaker
Martin Wechselberger
单位  Affiliation
University of Sydney
邀请人  Host
张祥
备注  remarks
Zoom number: 83367790049 Pin：231124
报告摘要  Abstract

In this talk, I present a coordinate-independent framework of geometric singular perturbation theory which goes back to Fenichel's original work, but hasn't received too much attention. I will motivate this point-of-view through biochemical reaction network problems which display distinct temporal features. In mathematical terms, such multiple timescale models are often singular perturbation problems "beyond the standard form" that require a  coordinate-independent framework of Fenichel Theory. We then present a corresponding parametrisation method for computing slow manifolds and their fast fibre bundles in such singular perturbation problems. In particular, we highlight the emergence of possible hidden timescales and show how our method can uncover these surprising multiple-timescale structures.
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修改:vinbo FROM 124.14.45.*
FROM 202.120.11.*

羡慕你会奇异摄动法

当年看别人用他来解板的大挠度方程，没看懂

【 在 vinbo 的大作中提到: 】
: 好评好评，原来奇异摄动有这种玩法，学习了
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FROM 120.230.66.*

看久以前看的文章了

当时觉得运算量太大，又不会符号运算的软件，就放弃了

【 在 vinbo 的大作中提到: 】
: 奇异摄动不难啊，我现在不会pde,不过奇异摄动本身你可以问我
: 奇异摄动其实就是，如果系统本身同时含有快尺度和慢尺度，那么可以降维分别研究快尺度子系统和慢尺度子系统，然后原系统的动态是两个子系统动态的和，外加一个误差。这个误差是O(epsilon）。这就是Tikhonov定理。
: 吉洪诺夫的弟子Vasil'eva用递归手法，把误差降到了O(epsilon^n).称为瓦西丽娃定理。
: ...................
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FROM 120.230.66.*