Neuroscience exploration - Differential Equations: The Language of Change

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 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 21:25 Sponsor: Brilliant.org 22:48 Outro ===== 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. #DifferentialEquations #DynamicalSystems #Mathematics _Description remastered: February 2026. Links & Bio updated; original context preserved._