MAE5790-6 Two dimensional nonlinear systems fixed points

Подписаться 11 тыс.

Просмотров 64 тыс.

50% 1

Linearization. Jacobian matrix. Borderline cases. Example: Centers are delicate. Polar coordinates. Example of phase plane analysis: rabbits versus sheep (Lotka-Volterra model of competition in population biology). Stable manifold of a saddle point.
Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 6.3, 6.4.

Опубликовано:

17 сен 2024

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 29

@harishankarmuppirala8189 4 года назад

"I'm gonna make up some stuff here, it's going to be approximately right" - A great Applied mathematician

@georgesadler7830 2 года назад

Professor Strogatz, this is another classic lecture on Two dimensional nonlinear fixed points which helps me to understand stable and unstable systems in Dynamics and Chaos. Phase plane analysis is another model that is important in Dynamics and Chaos.

@carolzhang5169 10 лет назад

Is the cameraman asleep??

@monsume123 8 лет назад

awesome hand writing! :)

@ruslanmukhamadiarov6705 5 лет назад

21:38 > "that get's your polar-coordinate mojo working" :DDDD

@Leonlion0305 3 года назад

7:01 boink lol this is why I love this prof

@jh-gp1cm 4 года назад

thank you :)

@pocanontas9242 10 лет назад

hello and thanx for the video! i have two questions 1. at 41:49 how do we find the NUMBER of fixed points? is there a theorem that predicts how many fixed points there are? i mean if the equation is difficult and we can't 'see' it, what do we do then? (send link if possible) 2. at 1:02:58, if we are on the fixed point (1,1) and we pertrube the system, do we know with certainty which way will it go? i mean is it a stochastic system or deterministic?

@Nikifuj908 9 лет назад

I don't know how to answer question 2, but for question 1, set the vector field/velocity field equal to zero (x' = 0, y' = 0); the solutions (x, y) are the fixed points.

@frankdimeglio8216 Год назад

@@Nikifuj908 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

@mohmtl 4 года назад

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

@erikumble 2 года назад

There are exercises in the book that are worth working through. You could also work through problem sets for similar courses that work through the book, such as math.mit.edu/classes/18.353J/ProblemSets/index.html there are also others on MIT OCW.

@sukranochani5764 Год назад

Thankyou sir

@tarikworku7908 3 года назад

I'm falling on your lecture so how can I get the text book that u use

@DelsinM 3 года назад

www.amazon.com/Nonlinear-Dynamics-Student-Solutions-Manual-dp-0813349109/dp/0813349109/ref=dp_ob_title_bk

@aakashdewangan7313 2 года назад

Was the camera person sleeping? He was not moving camera where the Prof. was pointing........😡😡

@markotomic7976 6 лет назад

Well, I understand when I get this type of equation x'(t) = x(t)*[x^2(t) + y^2(t) - 3] and y'(t) = y(t) *[x^2(t) + y^2(t) -3]. I use r^2 = x^2 + y^2, and then I find first derivative of r. But what can I do with these relations: x'(t) = x(t) * [9x^2 + 4y^2 - 36] and y'(t) = y(t) *[9x^2 + 4y^2 - 36].... I can't use this formula for r.... Please can someone explain me ?

@thomaskaltfuss9024 5 лет назад

You first outta do a coordinate transformation: r² = x² + y², x = r cos(phi), y = r sin(phi). Remember: z = x + yi = r exp(phi*i).

@noone4401 Год назад

The real lesson of this lecture is that it is fun to make weird noises. (30:30)

@relike868p 9 лет назад

How well does the LV system predicts populations in reality?

@TopGunMan 4 года назад

All models are wrong, but some are useful.

@davoodmomeni9644 6 лет назад

Any body know what is going happen for the fixed pt, when we transform the system from Cartesian coordinate to the polar? It seems that we can't talk about the fixed point in the polar coordinate anymore...am I right?