The Anatomy of a Dynamical System

[@wissalzaher4868]

the clarity in your style of delivering knowledge is priceless. I can binge watch your videos for hours, as a mechanical engineering student having access to this is a true blessing. This changes my whole perspective on life and makes this learning journey so enjoyable. I'm grateful for your contribution Professor :)

[@Eigensteve]

Thank you so much!!! Knowing that these are making a difference, and hearing stories like yours is so very rewarding. It makes it a true pleasure for me to make these videos!

[@naikshibabrat]

"Nonlinearity is what gives us job security in dynamical systems" Brunton 2021

[@vijanth]

What a statement indeed. It can be transalated in many ways

[@margheritacardelable]

Jjjjjbnbjhbjhj

[@margheritacardelable]

@@vijanth jbb

[@nyahhbinghi]

well, yes

[@intjengineering]

Some people say that the Uni you're in doesn't matter, that it all depends on you. Even I use to see it that way, and yes, that's true. You should be the main character, whether your Uni is a world first class institution or not. But then I come here and see the kind of Professors these top universities have. Whaaaaat a difference. Steve knows so much about System Dynamics, can explain so well, can engage, motivate you, and so on. Also, you see his passion for teaching. That's amazing.

[@psychii678]

This is one of the best introductions to dynamical systems someone could give

[@user-oj9rn3qx5e]

OMG I felt the whole universe being in my head after watching this

[@CallOFDutyMVP666]

It was 3am and I was about to sleep 💤but then Dr. Brunton uploads a video on nonlinear dynamics, I'm staying up! Excellent work as usual, in presentation. You can tell you know much about dynamic systems and we can read your passion. Thank you for your contribution to human knowledge!

[@chueri-dailydoseofshitposting]

Great lecture, even here in Brazil my professor recommended this video.

[@Eigensteve]

Awesome, thanks!

[@emiliew9357]

Amazingly clear and accessible explanation, thank you!

[@luisleal4169]

A complete course on dynamical systems from you would be a gift to humanity

[@chronicnerd8337]

Amazing work as usual Professor Brunton. I guess now I would also become extremely interested in Dynamical Systems as well. I have developed a great enthusiasm already in data-driven methods for engineering because of your lectures and your book. Thank you once again for sharing this extremely awesome content.

[@Eigensteve]

Thank you!

[@joseantoniogonzalezprieto2344]

These videos are extremely educative and really stunning, but they are also extremely beautiful. Please accept my gratitude for this invaluable contribution.

[@tylernardone3788]

Fantastic lecture! And a fantastic set of series on this channel thank you Professor Brunton!

[@Eigensteve]

Thanks so much!

[@louiskuta447]

These are fantastic videos. Thank you for making them public

[@jhightower]

Really wonderful presentation. It's a really unique talent to not only intimately understand mathematics and model building, but also having such intense aptitude to effectively educate any audience, particularly with a topic that can be sufficiently complex. Really well done. Very inspiring.

[@cronjej1]

Thank you so much for this primer. I really enjoy all your material and it is of great help to deepen my understanding of dynamical systems and control. I am currently working through your Control Bootcamp and the clarity in which it is done is next level!

[@iankay4081]

Hi Dr. Brunton, Been following your channel for a while, and I absolutely love the content you create and share! I am currently applying some of these concepts to farming and in designing I/O models for plant growth optimization.

[@Eigensteve]

So glad to hear it -- thank you!

[@Spiegeldondi]

Beatiful introduction and overview. Very enlightening and motivating. I am glad to have come across this channel!

[@isaacadjetey9618]

My passion for research ignited after watching this presentation.

[@juanpablocapossio5217]

Great explanation, thanks. I wish we could quote this video on our next paper on data-based models for fluidized beds.

[@umedina98]

Professor Brunton thanks, you are mi hero. Impeccable teachings.

[@simonbacaltos5660]

Thank you for the equation. It helped me think of my interest in human movement system. I'm thinking of the variables such as muscle fibers attached to the bone via tendons as well as the neural system including the brain as the primary control variable. However, when a neuromusculoskeletal system is dysfunctional the movement patterns becomes impaired and we see dysfunctional movement pattern emerging depending on the tissue at fault. It helps the physical therapists diagnosis.

[@bushracanaan5037]

thank you from the bottom of my heart

[@zoheirtir]

Amazing work as usual Brunton

[@gonzaloespinoza1279]

my friends this is gold 24K. first time i watch your content

[@muhammedakyuzlu6317]

so good so simple, Thanks for the effort

[@romanemul1]

Awesome presentation. An essential wiki. Thank you.

[@manuelmartinelandong253]

Great video! Regards from Oyala, Equatorial Guinea.

[@SRIMANTASANTRA]

Hi Professor Steve, 💕 lovely lecture 🙏.

[@igorstrozzi]

I also love dynamical systems and I love the way you so enthusiastically love them as well ^_^

[@fbkintanar]

17:20 "I strongly encourage you to start playing around with dynamical systems yourself. Pick a system you are interested in..." My dynamical system is lexical semantics in a brain-controlled uttering and perceiving hominin in a dialog pair or community. Brains have early percepts like vision, where there are activations in multiple feature maps, where the maps have topological correspondences to the geometric structure of the visual field as the hominin navigates a scene and acts on affordances of the environment (natural and social). Late percepts classify early percepts into types, where it is possible to track multiple instances of a percept-grounded type. Percepts, with early and late features, structure memory into some kind of repertoire or schema of visual object recogntion. At some point in hominin evolution, the emergence of language enabled the massive reuse of visual percept schemas into lexicalized concept schemas and vocabulary for visible objects. These noun-concepts are refined as participants in verb-concepts for the changing configuration of scenes involving objects of recognizable types. Noun and verb concepts provide the combinatorial raw material for planning and performing utterances that other hominins can recognize by their form and associate with conceptual content drawing on a shared schema of lexicalized concepts. Utterances could take the form of pantomime (think charades to get the audience to construe the content you are performing) or conventionalized sign language. At some point, communities agreed on small systems of phonemes that allowed the forms of noun-concepts and verb-concepts to be encoded in a sequence of consonant-vowel-consonant syllables, and gesture became less important as a carrier of content (unless you are in a Deaf community; the capacity for sign language is still there in all humans, it is just less frequently realized). How can this high-level conceptual model of a part of language be made into a family of interacting dynamical systems? I suspect state-space methods can be generalized to connect with the logic of formal linguistics in a way that is precise enough to implement the model in silicon. I am thinking of the work of Robin Cooper a U Gothenburg, which uses type theory with records to build on the work of logician Jon Barwise and philosopher John Perry. Jon Barwise and Jeremy Seligman wrote a book on state space models and "local logic". But how to locate the anatomical parts, challenges and uses of dynamical systems in a model of lexical semantics is still a big open question.

[@hennesey5928]

Damn U smart Frederick 😳🤝

[@Unidentifying]

love pretty much all your videos, great balance between math and physics

[@arthurm7846]

Great video Steve, thank you!

[@poincaretrajectories5917]

Listening after having my head broken by the Modern Koopman and Langevin Regression papers is a pleasure!

[@marwaeldiwiny]

Absolutely fantastic! Thanks Steve one of the favourite topics to my heart especially for smart materials and one of the important questions how can assess the beneficial and detrimental nonlinearities for systems.

[@komahanb]

The principle of superposition is used in conjunction with the principle of linerization (forming Jacobians around a given state x), so I guess that's not a big issue, as long as we solve nonlinear algebraic systems with repeated solutions of linear algebraic systems (Newton Raphson method). I like the way you explain scales of time. Great!

[@zinebkhoualdia609]

Thank you dr u have a flawless way to explain Thank u and really appreciate u sir

[@Eigensteve]

It's my pleasure

[@luthfiramadhan7591]

1 years ago wtf

[@CallOFDutyMVP666]

@@luthfiramadhan7591 he so smart he's 1 year ahead of human knowledge. Or he's been orbiting a supermassive blackhole and time dilation is responsible for this video appearing to be uploaded 1 year ago 🤔.

[@vinbo2232]

What happened to the "1 year ago"?

[@luthfiramadhan7591]

@@CallOFDutyMVP666 they are doing FTL travel we are just too stupid to understand it

[@artmusic6937]

thank you for sharing your knowledge!

[@varulsrivastava1693]

My brain's state isn't that different when I'm watching a video lecture versus when I'm asleep.

[@shawngonzales2073]

Thank you for these

[@Eigensteve]

Glad you like them!

[@HU5541N]

Good Explanation professor 👏

[@JousefM]

Great video Steve! :)

[@josealejandroleonsanchez7170]

I love your videos, keep it up!

[@danielpusicha7412]

Great video! One thing I especially love with math (and that is very applicable to dynamical systems as well) is when you can make it come to live so I would love to see a video with 'Techniques how to visualize a model'

[@michaelmarkoulides7068]

Thank you for making this video . I’m an engineer for over 20 years and recently I began modeling a system (for fun) for en ecommerce business ( one of my hobbies ). Sotake things like search volume impressions clicks sales etc to help assess an oppurtunity and ideally know when it’s too late or too early . I’ve tried to apply control theory concepts in the past but then I realised it’s a non linear system and knowledge of systems is on LTI and limited to physical systems which is easier to get the differential equations. This video helped me reframe the problem particularly because in this case I have the measurements but not the function space f . Do you have any other resources that you could point me to help me in making those decisions ? Thank you again this helped articulate my challenges and always had an intuition that my approach was limited but did not have the knowledge or language to express why and this video outlined that perfectly .

[@mike_field]

Thanks a lot for this Prof.

[@drillsargentadog]

One small quip--a state vector is neither unique nor minimal in general. Even in linear systems theory, there are many useful, nonminimal representations, and even minimal representations are only unique up to a change of coordinates. I would say the defining characteristic of a state vector is that it forms a complete description of the system (in a suitably understood sense) at any specific instant of time.

[@MaksymCzech]

Thank you for your videos

[@AG-cx1ug]

5:13 We don't have control over the Beta parameters - so how would we analyse the dependence of the dynamics on the parameters?

[@Jackisaboss1208]

You mentioned this lecture usually includes a discussion of machine learning based modeling and control of systems, do you have any recommendations for good content in this area?

[@parikshithk8289]

Hello Sir, I'm absolutely enjoying the way of ur teaching but i come from Electronics and Communication Engineering background u been giving examples related to mechanics and thermodynamics which courses in your playlist could help me to think better and get ahead in field one playlist that I'm learning from data driven analysis FS and FT Wavelets etc those are really making sense

[@Rodrigoviverosa]

A whole semester in 17 minutes

[@shashidharmuniswamy2620]

How will the differential equation describing the dynamical system change, with its evolution depending on history (memory) or previous state? I mean, Brain is a dynamic system of that sort? what changes now?

[@dr.gordontaub1702]

Great video!

[@shashidharmuniswamy2620]

Could you explain the difference between the control input 'u' and the 'beta' parameters, please? Suppose, I take a transistor, I would assume that the control input is the gate bias and one of the parameters is the geometry of the transistor. But on another hand, I can consider the gate bias to be a parameter too, depending on what my target measure is - say nonlinearity by harmonic and intermodulation products. The distinction is not clear to me.

[@arthurswanson3285]

U of Washington has excellent lecturers in Brunton and his co-author.

[@andrea3v]

If only my university lectures were like this...

[@raghavamorusupalli7557]

Teachers are unique in nature

[@komahanb]

I am interested in making videos on computational mathematics but don't really have the time and expertise for extensive video editing. I was thinking slides and screen recording - but I have to ask what technology do you use to make these videos?

[@ishangoinyambo6523]

Do we have a chronology of these videos am feeling like I could learn a lot here 🙌🏿

[@SalehElm]

Hi Steve. Really wonderful video. This might be a bit of a general question but given an anatomy of such DS (roughly we have structure + function), what do you think would be a "reasonable" approach to follow or take in order to quantify uncertainty (UQ) ... ? I gather this would highly depend on several of the involved components/parameters/variables you pointed out there, perhaps.

[@anthonyhibbert6304]

What are vectors?

[@lorenzovannini82]

Fascinating

[@Anujkumar-my1wi]

is there a difference between term configuration of a system and state of a system in dynamical systems?

[@johnsonoyero2855]

Awesome 👌

[@toanhockhaiphong]

How can you make it? I love this method.

[@eliklivnat9257]

Would you consider an hysteresis base system as data driven dynamically system?

[@krishnaaditya2086]

Awesome Thanks!

[@kennethcarvalho3684]

I could not understand the concept of optimization. Can someone throw light

[@mortenhattesen]

Is there any formal method to handling determination of past state from current state of a dynamic(al) system? Example: you know the location of a life raft floating at sea at time t. How do you estimate the (probability of possible) location of the life raft at time t-n? That would require using the inverse function of f(). But with f() being non-linear, you may find several possible f(x, t-n) leading to f(x, t), even without having disturbance, noise or chaotic behavior.

[@evileyes155]

Assuming you have a continuous dynamical system (like the one in the video). You can integrate backward to find the states in backward time. Roughly speaking. You don’t actually find the inverse function. With regard to the last part of your statement, assuming no noise and a smooth enough vector field, that won’t happen. As, roughly speaking, solutions would exist and are unique. This means that there is a one path the dynamical system would have to take to get to that specific starting state. There are cases where this breaks down like when your vector field is non-smooth or you add noise (a while different beast).

[@evileyes155]

To clarify, non uniqueness does not come from non linearly it comes from non-smoothness.

[@rickyhuang8745]

Many thanks for your lecture. Any example using your model?

[@necaro]

How will AI impact the future of research in Dynamical Systems?

[@lt4376]

so what about the anatomy of a static system?

[@swk229]

Thank you for all the amazing videos. Please machine learning and MPC with fuzzy logic.

[@Anujkumar-my1wi]

Just to be clear, 'state' of a system refers to information(set of variables) that fully describes the system at time 't', is it correct definition of 'state' of system?

[@andreichirap3259]

the MINIMUM set of variables that fully describes the system

[@Anujkumar-my1wi]

@@andreichirap3259 so if the previous 'n' states of a system fully describe the system at time 't' ,then those 'n' previous can be called as the state of system at time 't' because those previous 'n' states describe the system at time 't'

[@andreichirap3259]

@@Anujkumar-my1wi True, but these n variables should be the minimum number of variables that describe the system, for example, let's take a simple, and linear system [x1'; x2'; x3'] = [1 2 3; 5 7 2; 6 9 5]*[x1; x2; x3], in this example, we have 3 equations but only 2 equations are independent, the third equation is a linear combination of the previous 2, so the system can be fully analyzed only with the help of the first 2 states (x1 and x2)

[@Anujkumar-my1wi]

@@andreichirap3259 Thanks, and just to be sure when you said n variables there you were referring to the previous n states that together full describes the system ,beacuse state is a mathematical description that fully describes the system at time 't' in term of set of variables

[@Anujkumar-my1wi]

@@andreichirap3259 In, wikipedia state variables are reffered to as the varibles that describes the mathematical state of the system and describes state as something that descirbes the system ,but isn't state is the minimum set of varibels that describes the system wikipedia article link : en.wikipedia.org/wiki/State_variable

[@chivoronco4853]

Este tipo confunde sistema dinamico con equacion diferencial.

[@weert7812]

Great!

[@emmanuelameyaw6806]

Macroeconomists describes the economy using dynamical systems....fair representation of the real economy? What do you think?

[@anglonrx2754]

it's a brilliant way of representing the economy

[@murraypatterson9190]

Nonlinearity is a growth industry for mathematicians and provides them with job security.. In the real world of business most of us survive on using spreadsheet models which for the most part are linear, most of practical statistics is linear (aka General Linear Model) , many engineering problems can be solved using linear/matrix algebra etc etc. I realise in most of these cases are mathematics is trivial/uninteresting, but who cares if they work and give practical insights. Ps: this guy uses the psychological ploy of saying “good” “okay” at the end of the sentence to signal that he has explained something and we all perfectly understand what he means even though that may not be the case).

[@phillaysheo8]

okay

[@tuanleanh2759]

“d” should be non-italic because it looks like a function

[@jinishgaming3240]

❤❤❤❤

[@andie9589]

Pg 74

[@zrmsraggot]

Too bad there is no point to ask questions on here anymore ..

[@Eigensteve]

Please do feel free to ask questions. Sometimes I get pretty behind and miss some, but hopefully others have a chance to read and answer too.

[@zrmsraggot]

@@Eigensteve Oh wow ! It just felt like after 6 months+ and all the videos you posted since this one you didn't have time to go back on 'old' contents to answer questions and nothing more :) I hate to ask this since it's probably a dumb one but .. are all dynamical system outputs a derivative of the state w/r to time ? Thanks a lot for all of this ! I really love the way you teach it's crystal clear and I can feel your enthusiasm this is awesome

[@Eigensteve]

@@zrmsraggot That's a great question. I think of dynamical systems as a differential equation where the state changes in time (thus, dynamic). So for me a dynamical system is written in terms of the derivative (or second derivative) of a state with respect to time, equal to a function of the state. Maybe not everyone will agree with that exactly, but I think it is a good working definition. And thanks for the kind words!!

[@qwerty-tf4zn]

I feel like a thief. Taking away this knowledge for free..

[@DerekWoolverton]

I had to laugh when you proposed that the current moment's prices of all stocks might the "state of the system". Alas, as much as the "chartists" would like it to be so, it is nowhere near enough information. For just one stock, say "Gamestop" (ha), the possible state of the system might be the holdings of every individual Robinhood user, whether they're in the money, their bank account balance, how much leverage they're using (or options they have), the last time they checked reddit (in minutes), and how much fun they're having. Now that would make an interesting model.

[@drskelebone]

I question anyone working on this math and doing "super yacht" optimization. I get "a job that pays", but wtf. Making sure a billionaire doesn't pollute more than they already do? Ugh.

[@Giantcjy]

F i n a l l y