Introducing Bifurcations: The Saddle Node Bifurcation

Welcome to a new section of Nonlinear Dynamics: Bifurcations! Bifurcations are points where a dynamical system (e.g. differential equation) undergoes a significant change in its dynamical behaviour when a certain parameter in the differential equation crosses a critical value.

In this video, I explain saddle node bifurcations. These are bifurcations in which varying a parameter causes the appearance of a half-stable fixed point, followed by two fixed points from nothing. I discuss bifurcation diagrams, bifurcation points, and describe the concept of normal forms.

Questions/requests? Let me know in the comments!

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[AdityaPrasad]

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.

[joshuamercurio]

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.

[anilparmar]

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 ...

[ryleexiii]

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.

[pierreretief]

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

[trendytrenessh]

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

[eceoykuodabas]

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

[subhendukumarpatra]

Thanks for this amazing explanation professor ☺

[atinagg]

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

[yingliweng]

THANK YOU SO MUCH, THIS CLEARED OUT MY CONFUSIONS

[mdashfaqahmed]

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?

[kadajk]

Very helpful. Thank you for this video!

[farzanehazargoshasbi]

You are wonderful. Thank you so much❤️

[maryamfirdaus]

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

[indranilsen]

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

[CecaX]

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!

[اممحمد-قه]

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.

[parnianrezaei]

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

[abdellatifelbadraoui]

what you have use to write this tutoriel?

[saurabhkumar-zpxu]

how to do saddle node bifurcation in matlab using PSAT