Neuroscience exploration - Why Two Identical Neurons Behave Differently

To try everything Brilliant has to offer—free—for a full 30 days, visit https://brilliant.org/ArtemKirsanov . You’ll also get 20% off an annual premium subscription ===== My name is Artem, I'm a neuroscience PhD student at Harvard University. 🌎 Website and Social links: https://kirsanov.ai/ 📥 "Receptive Field" neuro-newsletter: https://artemkirsanov.substack.com/ ✨ Support me on Patreon to get access to Discord community: https://patreon.com/artemkirsanov ===== 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 📚 FURTHER READING & 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 ===== *Disclaimer:* This channel is my personal project. The views and content expressed here are my own and are separate from my research role at Harvard University. #neuroscience #dynamicalsystems #biophysics _Description remastered: February 2026. Links & Bio updated; original context preserved._