Fixed points and stability of a nonlinear system

[@ProfJeffreyChasnov]

Subscribe to my channel: kzbin.info

[@HumbertoFioravanteFerro]

Terrific explanation, professor. Thank you so much for making your video available to us!!

[@اممحمد-ق2ه]

Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.

[@jimmymacreator]

Great video. Clear, step-by-step explanation. Very much appreciated!

[@christepherclaxton665]

I am currently studying the Solow Growth Model in continuous time and this video does a fantastic job explaining stability in the steady state.

[@niftkislay]

Hello Mr. Christopher, I am also student of economics pursuing Ph.d. In the area of automation and it’s impact. We may have things to share and discuss. Looking forward to your response..

[@kixjock]

This video was extremely helpful. Thanks a lot!

[@اممحمد-ق2ه]

Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.

[@umbraemilitos]

This is a very good channel. I hope you get more viewership.

[@blockflight]

thx, this will defenitly help me on one of the questins of my exam on diffential equations.

[@اممحمد-ق2ه]

Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.

[@lucianoinso]

Just what I needed, thank you so much!

[@dev_escape]

Thank you sir, your explanation is great, I have my exam tomorrow.

[@physicsonyourscreenproblem575]

Wonderful explanation !

[@RustamBw]

for (1,1) point Jacobian Matrix, where he took (lambda square + 2*lambda -1 = 0) , i didn't understand? 10:00

[@MuddasirJahangir22]

Watch it with 1.25 speed :)

[@GTyellowjacket_aoe]

No, should be *1.5

[@vorpalinferno9711]

Wow.

[@thomaspogorzelski2688]

2.5x with extension gang. I do this for all videos tho cause i'm constantly drugged on caffeine

[@zainabsalah4815]

Thank u sm. ! This helped me alot with my exam !

[@xeoncore598]

excellent , very clear explanation

[@rfcano]

Very helpful and intuitive! Thanks a lot!

[@اممحمد-ق2ه]

Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.

[@ramiabou-shamalah3601]

At 15:00, you got -sqrt(2) because the first component of the jacobian was -1, and you did -1+ 1 - sqrt(2) = -sqrt(2), but how did you get the second component of V+? to be -2

[@ramiabou-shamalah3601]

Please and thank you Dr. Chasnov! Also, how did you find the corresponding vector to be 1 and then -sqrt(2) / 2?

[@saipcan17]

Thank you sir, this video helped me a lot!

[@deeptisharma9817]

thanks Sir,,for such a clear explanation.....

[@illuminatus639]

Was very helpful. Thank you.

[@patanmathematics5732]

Very good lecture.

[@اممحمد-ق2ه]

Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.

[@rmiller415]

First of all thank you so much for this video. Second of all I'm guessing you're using Blackboard to do this video, in which case those are some fancy lambdas for using a mouse and I applaud your blackboard abilities.

[@اممحمد-ق2ه]

Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.

[@20DoseOver]

you have just saved my ass...thanks

[@haekwonson5164]

Thank you so much for this awesome video

[@shaziedalam4074]

what website or software did you use to make the plots?

[@rakeshgautam1990]

Can we say that the Jacobian matrice for a nonlinear system is linear approximation of the system? or we just use it to find linear stability?

[@eddieliucp]

THIS HELPED SO MUCH THANK YOU!!

[@اممحمد-ق2ه]

Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.

[@fizixx]

Very nice, clear explanation. : )

[@اممحمد-ق2ه]

Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.

[@MrDeepakmore]

Please suggest good reference book for bigginers

[@anthonysegers01]

Excellent!!

[@missramz207]

nice explanation.

[@joef4309]

you use the magnitudes of the eigenvalues so some that you said were stable are incorrect. Please correct me if I am wrong. Very good video though sir, thank you!

[@اممحمد-ق2ه]

Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.

[@isultan]

What's the name of the app that you use for this presentation pleas?

[@poojabhakat8181]

Thank you sir...

[@bdizzle123001]

how did you generate the phase space diagram? I'm having trouble plotting that on matlab

[@ProfJeffreyChasnov]

Took some work. I think I used the analytic solution and varied the initial conditions.

[@bdizzle123001]

@@ProfJeffreyChasnov awesome I got it to work thank you! is the slope of the saddle point directions the Eigenvector where the x and y of the eigenvector are rise/run?

[@ProfJeffreyChasnov]

@@bdizzle123001 yes

[@bdizzle123001]

@@ProfJeffreyChasnov Thank you so much.

[@seppneimusser5723]

Thank's again^^

[@DumMeister]

May I know what is the reason for only considering x,y > 0 ?

[@ProfJeffreyChasnov]

These equations arise from considering competing species, and x and y are numbers of animals.

[@DumMeister]

Ah, fair enough. Thanks for the clarification. Great video!

[@adewuyiquadri2293]

its helpful but am still having problem with the fixed of points of tinkerbell map and bogdanov

[@nemernemer4494]

thank you ,

[@اممحمد-ق2ه]

Can you help please How classification of critical points of system in three equation in 3d

[@kaushikdr]

What are the derivatives of x and y with respect to?

[@ProfJeffreyChasnov]

time t

[@اممحمد-ق2ه]

Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.

[@ChiefEngr-GabsonAcademy]

You will never have a single thumb down, I wish

[@brycewalker1132]

Eigen Vectors for point (1,1) are v_+ = (- root(2), 1) and for v_- = (root(2), 1). Same outcome but wrong eigen vectors.

[@اممحمد-ق2ه]

Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.

[@اممحمد-ق2ه]

Can you help please How classification of critical points of system in three equation in 3d

[@malatalianaiidamane9550]

🎉🎉🎉🎉yes

[@malatalianaiidamane9550]

Yes🎉

[@GoldenMika]

What happened if my eigenvalues are complex? Both of them

[@ProfJeffreyChasnov]

Then you have complex eigenvectors also. If the matrix is real, then the eigenvalues and eigenvectors show up as complex conjugate pairs.

[@abhideepsingh4484]

if there are more then two equations?

[@ProfJeffreyChasnov]

Abhideep Singh Then you have a bigger matrix

[@quanteasy]

Abhideep Singh then there will be a n×n matrix and than you can find the equilibrium points. Here n represents order. If there is tri trophic than you have a matrix of order 3×3

[@marcfreydefont7520]

Is there a simple proof showing that the eigenvalues of the Jacobian are key in the determination of the fixed points stability. What about if the eigenvalues are imaginary?

[@اممحمد-ق2ه]

Hi and thanks a lot for your help! My problem is the following: I would like to draw a phase portrait for a system of 3 differential equations.

[@اممحمد-ق2ه]

Can you help please How classification of critical points of system in three equation in 3d

[@xiahua3811]

a fixed point of (2,0) was missing here....