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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 how the internal dynamics of neurons give rise to their remarkable computational properties. Through geometric reasoning about phase portraits and bifurcations, we'll gain intuition behind various phenomena, such as excitability, bistability, hysteresis and resonant oscillations.
Code for the video:
https://github.com/ArtemKirsanov/Youtube-Videos/tree/main/2024/Elegant%20Geometry%20of%20Neural%20Computations
Outline:
00:00 Introduction
01:26 Review of Hodgkin-Huxley equations
02:18 Deriving a 2-variable model
04:34 Phase Plane concepts
08:04 Excitability
12:14 Bistability and hysterisis
14:09 Saddle-Node Bifurcations
16:17 Andronov-Hopf Bifurcations
21:03 Integrators vs Resonators
22:26 Putting all together
25:15 Brilliant.org
26:17 Outro
References:
Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting by Eugene M. Izhikevich:
https://mitpress.mit.edu/9780262514200/dynamical-systems-in-neuroscience/
This video was sponsored by Brilliant