me - wordpress.com · 11/24/2020 · dijon field for ⻘们 i 您别 7 in ⼼ plane at every...
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I 7 Linear plan or system
荆⻔ 三 AM ________inx t y Lt Unknown functions
A hi 品 constant matrix
If I n.li is an eisenpair then
㑎⻔ ⼆ ⽐ El is asoli to ⼼
类1⽐ M ⼼ tl
teitlilze.it Alǔk inMeRecall i phase portrait for scalar autonomousODEguy o guy 70 g n o 类 9 y
33
fCCCI3ystationayptslg.es0
a Phase portrait for planar system
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Dijon fieldfor ⻘们 I 您别
7 In ⼼ plane at every
fiíǐiiii
rares g x yX
Case I i real distinct eigenvalues
⼋ ⼋ z.COalong Ū directionf f ly e Mi
y⼋ ŪdirectionL along I direction
iÜ
iiiinr.rs x ⽚ C iˋ
Citir7 direction converges toOhodd sink l similar to D stablecaseI faster as tsx
For linear system I is a stationary pt
Case 2 i real distinct eigenvaluesOL ⼊z ⼊
n
1
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n n7
rr 7 nodalsource
iii.it 品L 0ˇ 1 0 i
Case 3 real distinct eigenvalues⼋ o 2
1 V2 generalsolid7 7
iss.hessflsc.eMitczeidffii.ioTi
L rL r
LLCt.frL L Ysaddle unstable unless you start in i direction
When eigenvalues are complex
⼊ 2 r ⼟ ⼉ in 0 real
t.iiimassoli.iet i elm tint real t i Ǔimaset osu t t is in Ut Feat i i g
ttlosvt.vreaisinutiimeslzr r.ci
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ieMtlosut.iimgtsinvtir.atentire ǓzǓ Ǔz is a fundamental set of Solis
Case 4 u 0
sj iiii.inf V G so counter clockwise
toLCenter
Case 5 i m co Case 6ˊ_ o
L
其
spiral sinkspiral source
Draw phase portrait for
⻘⽵ A15 A 1名
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and determine type of stationary pt to O
de t l E I A det E 品 2 1 2 4⼋ ⼆ I ⼊z 4 wrsnodg
i 测 测 ⼼ 仙 派 13 v 2ˇ2 Y
了n 2 n 4 V
zvz 2ˇˋ 2Vz V1n_n
i Nil ⻔
n s.zffiresestse.inLL tf
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