Introducing Bifurcations: The Saddle Node Bifurcation 

I felt like crying. Such an amazing explanation available for free? I hope we have similar quality videos for every concept humans have touched. Thank you.

really glad you're back on this topic man. I'm actually doing my thesis on the nonlinear dynamics in epidemiological systems in relation to computer science, so getting a good grasp on all these is essential and hope to see more on this topic from you.

thank you... i had no clue about Non- Linear Dynamics and Chaos till yesterday .... and tomorrow morning i have a PG level exam for the same .... luckily yesterday i started seeing this lectures, i got some strength to study the detailed topics after seeing this... and now I'm confident for the exam ...

Y'all are so good at making this understandable. I'm a rising senior, but because I never really put effort into math classes before my sophomore year, I never had the opportunities to take advanced math classes; hence I'll never get to take a pre-calc, calc, or AP Calc class. Instead I'm stuck with stats and college algebra, which I will soon take. What I'm trying to say is, thank you, for communicating this information in a way people with less education and fewer opportunities can access and grasp.

Bloody amazing. This made no sense before watching this video and now it makes PERFECT sense. Thanks

Watching at a reduced playback speed of 0.75x was much more digestible and understandable pace, very thorough video and notes, great job! 👏

That was great!! Thank you so much for the effort! We look forward for the next video about bifurcations

thanks, great explanation, anyway may we have some topic on the hopf bifurcation later sir?

Amazing video, love the fast pace

Thanks for this amazing explanation professor ☺

It's a real GEM your videos !

Hi. I liked your videos very much. They are very well explained. Could you please make a video on andronov-hopf bifurcation and/or limit cycle?

Best video on Bifurcation theory

THANK YOU SO MUCH, THIS CLEARED OUT MY CONFUSIONS

Beautiful. But what to do with vectorial x, where the solutions cannot be computed analytically but only numerically? Newton Raphson does not converge near the biforcations!

thank you Mr Robot

Very helpful. Thank you for this video!

This is amazing thank you!

You are wonderful. Thank you so much❤️

Hi, Would you please upload the lecture on other types of bifurcation? It will be helpful.

Hello Professor . I have a system of three equations and I want to review the distinguished group, but my calculator is not very efficient. I ask you to help me, please.

love your video. Thx!

Isn't a fixed point one where f(x)= x? But here we've f(x) [i.e., dx/dt] = 0? Why?

wonderful!!! thank you!

amazing

Thank you very much :)

Very good explanation.

Really fantastic

Is there a reason why you call steady state a fixed point? fixed point has a different definition.. Fixed point is when f(x) = x where f is a mapping from R to R

hello! try to explain how to validate the law of darcy with navier stokes

how to do saddle node bifurcation in matlab using PSAT

what you have use to write this tutoriel?

from nothing to something thanks! wow

might wanna refer the book you took all this from...

0.75x

You lost me when the ad kicked in.