I'm sorry to hear your father suffered from Parkinson's, and I appreciate you sharing with us. I'm studying this topic as a PhD student under one of your former students, and I'm falling in love with this topic. Your teaching is outstanding, and I've been thoroughly enjoying and benefiting from the clarity of this series. Thank you!
DR. Strogatz, your lectures are amazing. Bifurcations , limit cycles ,stable and unstable points are important topics in Nonlinear Dynamics and Chaotic systems. I really love this applied mathematics topics and it's power applications to the real world.
I have some questions regarding the lecture 1. The professor has told, Saddle node, Trans critical and Pitch fork Bifurcations will happen when lamda = 0 and how the eigen values are changing with the equations? 2. For a>0, in Pitch fork Bifurcation, how we have got the unstable point suddenly. Can anyone please explain it clearly? 3. Can i know at all the places saddle node is an unstable node? Please solve the questions as I'm in a lot of confusion
+A.Naga Ranjith Kumar for the 1st question, i think we can use the bifurcation diagram to explain, stable means negative eigenvalues, unstable is positive eigenvalue. 2nd question, we don't have it suddenly, just imaging the picture that the stable origin(when a=0) split into 2 stable fixed points (a>0), left the origin still a fixed point, but got 'sucked' by stable fixed points at both side and therefore become a unstable fixed point.
As far as I know sir was talking about Img(Eigen values), I guess he missed that in his writing but in the diagram the shift that he talked about was with Img(Eigen Values) in mind. Please correct me if that isn't the case
LMAOOOOO uncollected HW, you fuckin know everyone is copying that shit MatchStackExchanged and TheoryExchanged and given 0 shit for their grade as they have a full answer on the site. #ModernEdumacation
I'm sorry to hear your father suffered from Parkinson's, and I appreciate you sharing with us. I'm studying this topic as a PhD student under one of your former students, and I'm falling in love with this topic. Your teaching is outstanding, and I've been thoroughly enjoying and benefiting from the clarity of this series. Thank you!
I'm doing my master's on brain computer interfacing. I hope we'll meet in future or maybe I may join you as a PhD student!!!
@@saanvisharma2081you two are in love 🤭
DR. Strogatz, your lectures are amazing. Bifurcations , limit cycles ,stable and unstable points are important topics in Nonlinear Dynamics and Chaotic systems. I really love this applied mathematics topics and it's power applications to the real world.
33:52 Hopf Bifurcation.
11:37 Awesome! Great Professor!
aww man, i wanted to hear about the exams
Deriving Supercritical Hopf bifurcation in cartesian coordinate:
textbook 2nd edition: page 253
λ =a (+/-) iω
(the book use μ instead of a)
I liked the "infinite period" explanation :)
Name of the book 44:33?
I thought the classes ended here but there's actually a bunch of others that are not in this playlist. Would be good if you could include them here
Why not just make the parameter another state element and kick up to 3d?
well explained!
Damn, i was here for transcritical bifercation. 20.55 and it was left out. Poor me 😢
The camera guy needs to pay attention better
May I ask does this professor teach some advanced courses?
You may ask.
@@Vicky-pb5hg 😂
I have some questions regarding the lecture
1. The professor has told, Saddle node, Trans critical and Pitch fork Bifurcations will happen when lamda = 0 and how the eigen values are changing with the equations?
2. For a>0, in Pitch fork Bifurcation, how we have got the unstable point suddenly. Can anyone please explain it clearly?
3. Can i know at all the places saddle node is an unstable node?
Please solve the questions as I'm in a lot of confusion
+A.Naga Ranjith Kumar for the 1st question, i think we can use the bifurcation diagram to explain, stable means negative eigenvalues, unstable is positive eigenvalue.
2nd question, we don't have it suddenly, just imaging the picture that the stable origin(when a=0) split into 2 stable fixed points (a>0), left the origin still a fixed point, but got 'sucked' by stable fixed points at both side and therefore become a unstable fixed point.
As far as I know sir was talking about Img(Eigen values), I guess he missed that in his writing but in the diagram the shift that he talked about was with Img(Eigen Values) in mind. Please correct me if that isn't the case
LMAOOOOO uncollected HW, you fuckin know everyone is copying that shit MatchStackExchanged and TheoryExchanged and given 0 shit for their grade as they have a full answer on the site. #ModernEdumacation