Differential Equations: The Language of Change

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My name is Artem, I'm a graduate student at NYU Center for Neural Science and researcher at Flatiron Institute (Center for Computational Neuroscience).

In this video, we explore the fascinating world of dynamical systems and differential equations, powerful tools for understanding how things change over time. We introduce key concepts like state variables, phase portraits, and limit cycles, using intuitive examples such as predator-prey models to visualize complex mathematical ideas.

Outline:
00:00 Introduction
01:44 State Variables
04:22 Differential Equations
08:24 Numerical solutions
11:52 Predator-Prey model
15:13 Phase Portraits
16:49 Equilibrium points & Stability
18:51 Limit Cycles
20:19 Conclusion
22:48 Outro

This video was sponsored by Brilliant

[macchiato_]

Your video on dendritic systems inspired me to study about neuromorphic computing, and then reservoir computing, and as an extension, dive deep into DEs and dynamical systems. It feels weird how the rabbit hole that started me on my journey has caught up to me 😅😅

[quecojonesq]

I love you man, please keep at it. I cannot stress enough how useful and informative your videos are. You deserve the world for this work.

[bhaveshsuthar]

Learned yesterday about Hopfield networks from ur video.
And today John Hopfield & Geoff Hinton wins 2024 physics Nobel prize.
Keep making in-depth videos on such topics Artem, they’re very intriguing.

[Tom-spgy]

This is the best channel on computational neuroscience ever!

[ismailhasan]

The astounding visuals makes the video hundred times more interesting. Love your work.

[yashwantherukulla]

where were you 4 months agoooo 😭😭I really needed this vid for a course in my previous semester. thnx for making and as always excellent quality! I hope nothing but the best happens to you 😄

[kikumayumi]

Beautifully simple yet perfectly explained

[atommax_]

Feeling kinda proud that I knew all math in the video in my 16, and also reminded that I haven't studied DE for a few month already.

Your videos are amazing, i find answers for exact questions that bothered me for a long time. Thank you

[lunafoxfire]

These videos are consistently amazing! Very excited for the next in the series! Getting into the actual math/dynamics of a neuron seems _extremely_ fascinating!

[xXCindellaXx]

Underrated chanel, love to hear that more is coming up

[pavlovsdawg]

doing brilliant work spreading the beauty of computational neuroscience as always. as a physics major doing comp-neuro research, your videos synthesize topics in math, physics, and biology together very well and are a must watch for any who seek a deeper understanding of electrophysiology and neural networks. perhaps the next hopfield is a member of this lovely community :)

[foreverjoyous]

Awesome stuff! Would love to see how this can be used to visualize recurrent neural network activity!

[mattthelearner]

I’m sharing your channel to everyone I know… Come on guys we need Artem’s channel to grow!

[gman]

Brother you have a knack for this. Keep up the good work, love your videos 👍🏻

[veniasblack]

Loved how he simplifies the topic to be suitable for people who have no stomach for math.
Is there any book recommended to study differential equations in the same way he did?

[zacharyboschbird]

This is so intuitive youre hella creative

[dan_pal]

Impecable explanation, as expected from Artem. Thanks for another great video

[watcheroffunnystuff]

Your channel is of such a high quality, I hope to be able to convey my ideas with such skill one day.

[douglasstrother]

I first got turned-on to this stuff when studying the Duffing Oscillator in my Classical Mechanics class. Dynamical Systems put the WOW! back into Physics for me.

[TiborVass]

Keep these gems coming! Can't wait to watch your next videos!