Nonlinear odes: fixed points, stability, and the Jacobian matrix

An example of a system of nonlinear odes. How to compute fixed points and determine linear stability using the Jacobian matrix.
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[@luci7061]

7 years later and this is going to save me on a final!

[@notcrediblesolipsism3851]

Easily the most succinct video of any maths concept I've ever seen. Fantastic, thanks.

[@virusalgebra33]

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[@electricbill872]

Almost 8 years later and you are still helping out people

[@lingarajpatnaik3870]

Most simple, peaceful delivery of a sophisticated area of maths! Regards Sir.

[@umarbashir7196]

I was very impressed with the explanations. Thank you for the knowledge sharing

[@corynllamoza42]

you sir.. just save my semester!!! God bless you very much:)

[@griffinlastname743]

Thank you for being so concise and eff

[@gabriellefortune4627]

This literally saved my life an hour before an exam, thank you

[@ts4124]

Thank you! that helped me a lot with my study

[@mrproxj]

Thanks dude, really helpful

[@smarttennisguy10]

great video!

[@wejdan_1i408]

شرح ممتاز، شكراً لك.

[@Zavintyshka]

Thanks to this video, I understood how to do it all. Hello from Russia :)

[@avalpreetsingh2688]

Nicely Explained
Thanks

[@blackdice1001]

Thank you!

[@seppneimusser5723]

Thank you so much, you helped me^^

[@johnbrownell1]

Thank you so much for this. My prof skips almost every step and assumes that it is common sense to be able to deduce this stuff

[@zoeyzhao4403]

me too😢

[@tenton2000k]

You're a god. Holy shit thank you for this video.

[@sarahkafel1883]

Please professor video for
Nonlinear fixed point stability and the Jacobian matrix four dimensions
I really need a video of four equations with four variables

[@vitokonte]

Why did you calculate the eigenvalues for last equilibrium points but not the first 3?

[@sarahkafel1883]

Please professor video for Nonlinear analysis fixed point stability and the Jacobian matrix four dimensions
I really need a video of four equations with four variables

[@JoseLuRu]

Good video. I have a question .
Would you help me with this system finding out if it is stable or no stable?
dot X1= 0.5-(X1)^0.5
dot X2=(X1)^0.5-(X2)^0.5

[@muhammadzainkhan557]

hi, what software you use for solving this question? (means writing down)

[@tenton2000k]

So saddle = unstable?

[@hgfygcfg177]

👍👏

[@AchiragChiragg]

What is a fixed point?

[@blackclover4375]

What happens if the eigenvalue of the jacobian matrix is zero

[@ProfJeffreyChasnov]

Then stability is neutral.

[@blackclover4375]

@@ProfJeffreyChasnov what does that mean in terms of the behaviour of the vector near the critical point?

[@ProfJeffreyChasnov]

@@blackclover4375 It circles around the critical point, not moving closer or further away.

[@hayes1729]

@@ProfJeffreyChasnov I am no expert, but this sounds wrong. I believe there will be counterexamples even in dimension 1, where there is no "circling around." I think you either have to examine higher order derivatives, or look at how the Jacobian behaves in the vicinity of the fixed point.

[@rehaballawi6969]

منو هنا اختصاصه نظم