MAE5790-2 One dimensional Systems

[@ShyamDas999]

Prof. Steven Strogatz's lectures are amazing. I have learned nonlinear dynamics through his lectures. Thanks to Cornell University for documenting these lectures and uploading them on KZbin.

[@AlePreludioFinal]

The perfect complement to the book!

[@carolinestepanik]

God Bless these videos!!!

[@georgesadler7830]

DR. Strogatz, thank you for an awesome lecture on Linearization for 1-D systems and Bifurcations analysis of nonlinear systems. These lectures are very entertaining.

[@kc-cn8zy]

Thank you Prof Strogatz, wonderful series.

[@bengalbasi4753]

American professors are real professors. The more I try to understand them, I realize atleast I have NOT seen a "professor " in my student life here in India... I have read a few excerpts from professor Steven Strogatz's infinite powers. I believe such books should be made known to students here in India who wants to pursue serious science in future. Such books by such a top notch professor are a must read for everyone.. Experts, non experts, layperson (like myself ) , students.

[@frankdimeglio8216]

WHY AND HOW GRAVITY AND TWO DIMENSIONAL SPACE ARE CONSISTENT WITH WHAT IS E=MC2: E=MC2 is taken directly from F=ma. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! The TRANSLUCENT blue sky is manifest as (or consistent with/as) what is BALANCED BODILY/VISUAL EXPERIENCE. Accordingly, ON BALANCE, the TRANSLUCENT blue sky is true/real QUANTUM GRAVITY !!!! THINK !!! ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). Accordingly, ON BALANCE, the rotation of WHAT IS THE MOON matches the revolution. Importantly, what is GRAVITY is an INTERACTION that cannot be shielded (or blocked) ON BALANCE. Great. You didn't forget to consider what is the orange (AND setting) Sun ON BALANCE, did you !!!!? Magnificent. I have FUNDAMENTALLY and truly revolutionized physics. (Lava is orange, AND it is even blood red.) GREAT !!!! Obviously, carefully and CLEARLY consider what is THE EYE ON BALANCE, as it ALL CLEARLY makes perfect sense ON BALANCE !!! (BALANCE AND completeness go hand in hand.). Fantastic !!! The stars AND PLANETS are POINTS in the night sky. What is E=MC2 IS dimensionally consistent !!! The density of what is THE SUN is then necessarily about ONE QUARTER of that of what is THE EARTH !!! INDEED, notice what is the fully illuminated (AND setting/WHITE) MOON ON BALANCE !!!! What is E=MC2 IS dimensionally consistent !!!! Indeed, TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! CLEAR water comes from what is THE EYE ON BALANCE !!! Excellent. Think. By Frank Martin DiMeglio

[@asdfafafdasfasdfs]

One can give praise without being self deprecating... several reasons for this, including that this is a global top professor not virtue of being American vs Indian.

[@redrum41987]

It's great I found these videos, they are really going to help with my applied ODE class that is focusing on dynamical systems.

[@ThePaulTM]

RedRum won the Grand National in the UK I think it returned 33 to 1. You will find that waves come from 3 inner cicle diags to one circle, and different waves from 2 inner circle diags. in one circle. They show 5 plus 5 or 10 vector wave arrangements. This is in 3D. This will keep repeating in size and with combo of both. This will keep you going til Xmas. Paul

[@frankdimeglio8216]

​@@ThePaulTM WHY AND HOW GRAVITY AND TWO DIMENSIONAL SPACE ARE CONSISTENT WITH WHAT IS E=MC2: E=MC2 is taken directly from F=ma. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! The TRANSLUCENT blue sky is manifest as (or consistent with/as) what is BALANCED BODILY/VISUAL EXPERIENCE. Accordingly, ON BALANCE, the TRANSLUCENT blue sky is true/real QUANTUM GRAVITY !!!! THINK !!! ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). Accordingly, ON BALANCE, the rotation of WHAT IS THE MOON matches the revolution. Importantly, what is GRAVITY is an INTERACTION that cannot be shielded (or blocked) ON BALANCE. Great. You didn't forget to consider what is the orange (AND setting) Sun ON BALANCE, did you !!!!? Magnificent. I have FUNDAMENTALLY and truly revolutionized physics. (Lava is orange, AND it is even blood red.) GREAT !!!! Obviously, carefully and CLEARLY consider what is THE EYE ON BALANCE, as it ALL CLEARLY makes perfect sense ON BALANCE !!! (BALANCE AND completeness go hand in hand.). Fantastic !!! The stars AND PLANETS are POINTS in the night sky. What is E=MC2 IS dimensionally consistent !!! The density of what is THE SUN is then necessarily about ONE QUARTER of that of what is THE EARTH !!! INDEED, notice what is the fully illuminated (AND setting/WHITE) MOON ON BALANCE !!!! What is E=MC2 IS dimensionally consistent !!!! Indeed, TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! CLEAR water comes from what is THE EYE ON BALANCE !!! Excellent. Think. By Frank Martin DiMeglio

[@ThePaulTM]

@@frankdimeglio8216 Thank you Frank. The more you study how things go together its only then that you can appreciate the wonderful 3 dimensional order to things.

[@ejdansu]

Such a great teacher! Thanks Prof!

[@ahmedamr5265]

Thanks a lot! I consider myself lucky to have the chance to learn from your classes :)

[@mohamedbadaoui8868]

Thank you Prof. Steven Strogatz's.

[@martinsaravia]

This is a true gem...

[@luissoto4525]

The best explanation I have ever seen :O THANKS!!!!

[@JamesVestal-dz5qm]

The professors showed a lot of forgiveness because they love the truth!

[@zphuo]

@1:08:30 why r

[@lucakolibius1468]

Chapter 3 starts at 32:20

[@FarhanKhan-ed8ro]

can you tell me the book name that prof. use in his lecture

[@lucakolibius1468]

@@FarhanKhan-ed8ro he authors it and it's called something with dynamical systems. You should be able to Google that easily.

[@weishanlei8682]

1:14:57 tongue lips. For saddle-node bifurcation, number of fixed points, for r from negative to positive, should be 2 to 1 to 0.

[@theodoremercutio1600]

No, it can go in either direction. It depends whether you're sliding are from positive to negative or vice versa. So both 2, 1, 0 and 0, 1, 2 are correct desceiptions

[@srikanthgopalan1593]

Is there a typo in the book? It specifies the first bifurcation example discussed as xdot = r - x^2 and then the discussion about fixed points for r >0, r = 0, and r < 0 don't follow in the book. In the lecture here since xdot = r + x^2, it makes sense.

[@hanumanbearpig]

Great videos!

[@DaroG35]

Based on the great Andronov old book "Theory of Oscillators" One dimensional system dx/dt =f(x) can oscilate if f(x) is real multivalued function eg. when f(x) presents closed loop shape. If f(x) is single valued real function there is no oscilations.

[@shuangmiao2929]

24:44 You didn't talk about the initial condition, so the uniqueness doesn't even make sense here.

[@JRush374]

At 22:00 that left unstable point would only exist in a pure mathematical sense. But in the real world it wouldn't because if you have 0 bacteria the number of bacteria wouldn't increase. X>=1

[@PymGordonArthur]

Thank you very much.

[@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 as f(x) = x or standard notion is T(x)=x as given by Banach fixed point theorem. 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.

[@yifuxero5408]

. The four simplest cases are:: 1. x^2 - 2, seed 2*cos(k*Pi/N), N is odd, 2.. (x^2 - 1) / (2*x), seed cot(k*Pi/N), and the iterative logistic map 4*x*(1-x), with seed sin^2(k*Pi/N). For any given N, say 7, the results are the same as to the periods. Results for the first few N: (3, 5, 7, 9, 11, 13, and 15) are respectively (1, 2, 3, 3, 5, 6, and 4). Feel free to try it with N = 7. You'll get period 3 for each.

[@pettPette]

I enjoyed this.

[@Odysseusf]

Fantastic!

[@Odysseusf]

bookmark:33:36

[@siaahmadi413]

10:47 but what if the derivative of f is on the order of eta while its second derivative is on the order of sqrt(eta)?

[@derekxiaoEvanescentBliss]

Eta is your small variation around a fixed point (or really any chosen point). If, for a chosen maximum eta, your f'' turns out to be roughly f'/eta*2, such that f''*eta^2/2 ~ f'*eta, ie the if it turns out that FOR A GIVEN ASSUMED MAXIMUM ETA (for example eta

[@LenBerman]

What are possible sets of fixed points in 1D as f varies. Awaiting book.

[@benmyers4279]

Impossibility of oscillation only works if f(x) is real. If we have an equation dx/dt = ix, then we get x(t)=exp(it)

[@zeldovich33]

He defines in the first class that the treatmens on one dimensional flows are for f(x) thar are real

[@JamesVestal-dz5qm]

So blank is really small and from here we'd like to neglect the blank term!

[@lemons107]

Brilliant

[@michaellewis7861]

Aren’t you continually assuming a specific time relation between either the evolution of x with time or x dot with time when making the graph?

[@aneet84]

Hmmm... I wonder what chalk he uses on his chalk-board. Hagoromo? Didn't look like it. I would very much like to know!!

[@JamesVestal-dz5qm]

Why does u of m love differential equations so much?

[@mohmtl]

Hi I would appreciate the help of someone who took the course or has the material to provide me with the assignments or problem sets in this course which are typically chosen from the textbook just problem numbers from the textbook for each assignment. Kind regards

[@iconjack]

At 11:05, η² might be small, but how do we know f''(x*) is not huge enough to make the product significant?

[@yiwensin5913]

Then just choose η to be small enough so that the f' term is negligible.

[@shirou9790]

Well, since f''(x*) is a constant whatever the value of η, we do have that f''(x*).η² converges towards 0 faster than f'(x*).η as η→0.

[@zeynepadguzel2131]

sorry.how to draw rx-e^x diagram.can you help me

[@handledav]

wow

[@solonsaoulis5290]

Looks like the sound is blocked...

[@mohitoness]

how does this "exchange of flavors" look in 3d??

[@JamesVestal-dz5qm]

Harmonic oscillator is a truncated Taylor series

[@brendawilliams8062]

Thankyou

[@wiemabichou5840]

Someone knows where I find the course notes, please???

[@yiwensin5913]

Nonlinear dynamics and Chaos - Steven Strogatz (his own book). He mentions it in the first lecture.

[@xaviervangorp4862]

27:50 : Solution by the method of perfect drawing cause I'm a god

[@DanGM123]

strogatz is da man

[@mabdinur85]

Maybe better to call them a trident instead of a pitchfork?

[@hanyerfan8204]

really gud :)

[@awsumpersun321]

x' = x + dirac(x-2) first order ODE that is periodic?

[@teclishighelf5787]

@17:53 is "honest to god" a technical math term? Could you please demonstrate a dishonest to god unstable fixed point in order to clarify the difference? Could you demonstrate an honest to Satan fixed point?

[@tumadre259]

don't cut yourself with that edge

[@Mahmood42978]

@@tumadre259 I sense Teclis High Elf wears a fedora and identifies as an "Incel"

[@tolaneco]

Room for improvement in camerawork.

[@marshallmykietyshyn4973]

I'm sorry, physicists are "cavalier" about mathematical rigour? As an engineer, I object.

[@Hexanitrobenzene]

It probably depends on the particular field of physics. Applied fields tend not to worry, because real world measured quantities most of the time are described by well behaved analytical functions. Theoretical fields most probably do, otherwise one could get paradoxes in theories.

[@JamesVestal-dz5qm]

Christine aikens bra ket book was super confusing

[@Harmonyano]

mark 22:13

[@JamesVestal-dz5qm]

Obama did look at the data and I got into rank 1 under Obama because I have good genetics!

[@ThePaulTM]

I show that 3d geometric DNA and Wave strings are generated from the very start of creation in helical form In super perfect order. This can explain the non-linear Lorenz Effect in which mathematicians decide that everything is Chaos. Please say If I am wrong & explain how our nose goes between our eyes from Cornell to the butterflies in Hong KONG?

[@fgeng3828]

I don't really see the point in attacking the chaos theory to establish a 3D order. The existence of chaos doesn't immediately prescribe it as the dominant form. The visualisation tool adopted by Poincare is just as effective in analysis of either chaos or order. And the notion of stability is certain an essential cornerstone for any order,be it 2d or 3D.

[@ThePaulTM]

I am not really attacking the chaos theory because it is just a load of baloney. There is a perfect PLATONIC ORDER for DNA that you find difficult to accept. There is no mention of a system of order called CubicWonder you only focus on your fractal systems of disorder. The Lorenz effect started your theory of chaos but I have shown I can produce a similar effect with 3d geometric order. If 100,000 cars jam up the city centre it can be called chaos but later in the evening the chaos is gone. I think you ignore the discoveries that I have made of a perfect 3D order because you as scholars missed out. You keep hyping up chaos and pretend the 3D order I show does not exist. So then if chaos is so, can it start small like a little shape. What colour is it and how much does it weigh ?

[@fgeng3828]

Can you please provide a phase space of CubicWonder for possible analysis?

[@ThePaulTM]

I show how it goes together on my videos. When you say you want a phase space. This system provides all the waves to infinity such as DNA, sound or electricity. I have shown for years how 3 phase electrical helical waves come from a string of cubes in 3D they are not flat like in a book. You will have to decide what you want to study. CubicWonder is a part of the Platonic system of order. Study my videos and you can decide exactly what to work on.

[@fgeng3828]

The reason I ask for a phase space is it helps to visualize the trajectory of the system. I understand you have your own formalism but you need to boil that down to a set of differential equations (or some generalised form) that specify your system in a phase space, otherwise we can't apply traditional approach to analyse it. About myself,, I'm currently studying my bachelor degree in Molecular Biology.

[@ThePaulTM]

Are the questions that I asked being analized to give me an answer? They are perfect 3D reality in 3D geometry. I was hoping you could have said something because Plato said everything comes out of geometry. This 3d geometry gives us 3 types of DNA & proves non-linear stuff not being chaos. These discoveries should at least be given some sort of answer from Cornell. Unless you are all sure about the chaos with no use for this Plato 3D fractal order & DNA geometry that comes from a system of order called CubicWonder. Paul

[@ThePaulTM]

It would be nice if the scholars of Cornell can come up with an answer to my questions about the perfect order I show that is not chaos. Why are you looking down your noses at these major discoveries that show DNA 3D geometry is concentrical around the 10_20 vectors for a perfect system using Plato 3D geometric order. These new finds are practical and logical in 3D reality. Why is it so much trouble for your brillient mathematicians to come up with an answer to admit that your theories about a system of chaos is nothing but load of nonsense? Hope to hear from Cornell in 2015. Paul

[@ThePaulTM]

It is better if I talk to a wall, Stay with your chaos and keep selling to people who do not understand 3D. You know it will run out of steam or they could ask for their money back.

[@mohitoness]

ThePaulTM of course it is of a perfect and higher order, because math is limited by our way of interacting with our sense data and the world, and is only there to be able to explain it in a very particular way. But its limitations are also its strengths; isn't that what makes us human?

[@ThePaulTM]

Thank you, We are looking at a wonderful system of 3D geometric order that is impossible to imagine by just using equations. We are just begining to scratch the surface of this 3 dimensional system that is of super perfection & was taught by Plato. Up until now academics do not show enough order for a little finger. Why would they keep pushing 2D chaos and have no interest in 3D order ?

[@danlurny4129]

+ThePaulTM Maybe there are some geometrical restrictions in the processs of DNA formation, so we need to include this restrictions to add to the equations to solve more complicated problems&lt; which are biological problems. But mathematical way itself is rigorous and we trust it. I don't see contradictions. To solve problem we need to know what is a region in which we solve our problem. But we don't know a lot. Science оust keeps going and try out different methods. Century ago we didn't know about many things. Don't accuse anyone. Iluminati NOT exists)

[@JamesVestal-dz5qm]

This class sucks thermo is way trippier