Nonlinear Systems: Fixed Points, Linearization, & Stability

[@lionelinx7]

Very good series, has helped me a lot!

[@ProfessorRoss]

Glad to hear it! Thanks for watching.

[@jerrysu8119]

Explanation better than my prof

[@江百川]

I really like all series of your video. But there is a writing mistake at 3:05, and maybe it should be: f(x^* +u, y^* + v). I just want to remind other learners.

[@ProfessorRoss]

Thank you for this correction and the previous one. I've put them in the video description. I'm glad the videos have been helpful!

[@kamugishajoseph5914]

very helpful thanks

[@advancedappliedandpuremath]

Hi Sir hope you are having great time. I have a question regarding fixed point. In context of a function fixed point is defined where f(x) = x or standard notion is T(x)=x. But in context of dynamical system when we use the word fixed point it seems that it doesn't relate to definition T(x) = x but rather we say that fixed point is where the derivative is zero. So my question is that does the word fixed point meaning differs in both contexts or is there any analogy.

[@rewirestrike]

Amazing

[@frimpongemmanuel6098]

what if there were trig function on the right hand side (e.g cos(x) or sin(y) ), do we have to include it ??

[@ProfessorRoss]

Yes. Following the procedure here you would take the derivatives of those functions, evaluated at the fixed point, to construct the Jacobian matrix A (6:09). For example, if (x,y)=(0,0) is your fixed point, d[cos(x)]/dx = -sin(x) = 0, since we're evaluating at x=0, and d[sin(y)]/dy = cos(y) = 1, since we're evaluating at y=0, etc.

[@wentaowu3070]

I wonder if they could plug the advertisements in the beginning and end of each video. I am focusing on your lecture, suddenly an advertisement. It is scary and annoying.