Neuronal Dynamics Self-Study Curriculum

An 8-week self-guided study plan based on Wulfram Gerstner's Neuronal Dynamics course at EPFL.

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Resources

Resource	Link
Video Lectures	MOOC All Lectures
Online Textbook	Neuronal Dynamics Online
Python Exercises	Exercise Documentation
edX Course (Free Audit)	EPFL Neuronal Dynamics on edX
Teaching Materials	Lecture Slides & Materials

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Weekly Study Routine

Day	Activity
Monday	Watch video lectures
Tuesday	Read textbook chapters
Wednesday	Generate NotebookLM podcast from Nicholls chapters
Thursday	Review notes, revisit difficult concepts
Friday	Complete Python exercises

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Week 1: Introduction & The Leaky Integrate-and-Fire Model

Estimated Time: ~5 hours

Video Lecture 1: A First Simple Neuron Model (83 min)

Part	Topic	Duration	Link
1	Neurons and Synapses: Overview	10 min	Watch
2	The Passive Membrane	21 min	Watch
Math	Linear Differential Equation	22 min	Watch
3	Leaky Integrate-and-Fire Model	8 min	Watch
4	Generalized Integrate-and-Fire Models	17 min	Watch
5	Quality of Integrate-and-Fire Models	5 min	Watch

Textbook Reading

• Chapter 1: Introduction - Neurons and Mathematics
  • 1.1 Elements of Neuronal Systems
  • 1.2 Elements of Neuronal Dynamics
  • 1.3 Integrate-And-Fire Models
  • 1.4 Limitations of the Leaky Integrate-and-Fire Model
  • 1.5 What Can We Expect from Integrate-And-Fire Models?

Python Exercise

Exercise	Description	Link
Leaky Integrate-and-Fire	Simulate LIF neuron, inject currents, measure firing rates, explore f-I curves	Exercise

Key Concepts

• Membrane potential and resting potential
• RC circuit analogy
• Leaky integrate-and-fire (LIF) neuron model
• Spike threshold and reset mechanism

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Week 2: The Hodgkin-Huxley Model

Estimated Time: ~5 hours

Video Lecture 2: The Hodgkin-Huxley Model (77 min)

Part	Topic	Duration	Link
1	Biophysics of Neurons	5 min	Watch
2	Reversal Potential and Nernst Equation	11 min	Watch
3	Hodgkin-Huxley Model	23 min	Watch
4	Threshold in the Hodgkin-Huxley Model	26 min	Watch
5	Detailed Biophysical Models	12 min	Watch

Textbook Reading

• Chapter 2: Ion Channels and the Hodgkin-Huxley Model
  • 2.1 Equilibrium Potential
  • 2.2 Hodgkin-Huxley Model
  • 2.3 The Zoo of Ion Channels

Python Exercise

Exercise	Description	Link
Hodgkin-Huxley Model	Simulate HH neuron, explore gating dynamics, modify channel densities, find threshold currents	Exercise

Key Concepts

• Nernst equation and reversal potentials
• Voltage-gated ion channels (Na⁺, K⁺)
• Gating variables (m, h, n)
• Action potential generation mechanism

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Week 3: Synapses, Dendrites, and the Cable Equation

Estimated Time: ~5 hours

Video Lecture 3: Synapses, Dendrites and the Cable Equation (69 min)

Part	Topic	Duration	Link
1	Synapses	15 min	Watch
2	Synaptic Short-Term Plasticity	9 min	Watch
3a	Dendrite as a Cable	11 min	Watch
3b	Derivation of the Cable Equation	10 min	Watch
4	Cable Equation	10 min	Watch
5	Compartmental Models	14 min	Watch

Textbook Reading

• Chapter 3: Dendrites and Synapses
  • 3.1 Synapses
  • 3.2 Spatial Structure: The Dendritic Tree
  • 3.3 Spatial Structure: Axons
  • 3.4 Compartmental Models

Python Exercise

Exercise	Description	Link
Passive Cable	Simulate passive dendrite, explore electrotonic propagation, compare myelinated vs unmyelinated	Exercise

Key Concepts

• Excitatory vs inhibitory synapses (AMPA, NMDA, GABA)
• Synaptic facilitation and depression
• Cable equation and electrotonic spread
• Multi-compartment neuron models

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Week 4: Phase Plane Analysis & Bifurcations

Estimated Time: ~6-7 hours

Video Lecture 4: Two-Dimensional Models and Phase Plane Analysis (165 min)

Part	Topic	Duration	Link
1	From Hodgkin-Huxley to 2D	18 min	Watch
Math 1	Separation of Time Scales	11 min	Watch
Math 2	Exploiting Similarities	16 min	Watch
2	Phase Plane Analysis	17 min	Watch
3a	Analysis of a 2D Neuron Model - Pulse Input	12 min	Watch
3b	Analysis of a 2D Neuron Model - Constant Input	9 min	Watch
Math 3	Stability of Fixed Points	19 min	Watch
4a	Type I and Type II Neuron Models	16 min	Watch
4b	Firing Threshold in 2D Models	21 min	Watch
5	Nonlinear Integrate-and-Fire Model	16 min	Watch

Textbook Reading

• Chapter 4: Dimensionality Reduction and Phase Plane Analysis
  • 4.1 Threshold Effects
  • 4.2 Reduction to Two Dimensions
  • 4.3 Phase Plane Analysis
  • 4.4 Type I and Type II Neuron Models
  • 4.5 Threshold and Excitability
• Chapter 5: Nonlinear Integrate-and-Fire Models

Python Exercises

Exercise	Description	Link
Phase Plane Analysis	Plot nullclines, find fixed points, analyze FitzHugh-Nagumo dynamics, compute eigenvalues	Exercise
Type I and Type II Neurons	Compare f-I curves, identify threshold behaviors, classify neuron types	Exercise
Exponential Integrate-and-Fire	Simulate EIF model, find rheobase current, plot strength-duration curve	Exercise

Key Concepts

• Nullclines and fixed points
• Saddle-node and Hopf bifurcations
• FitzHugh-Nagumo model
• Type I vs Type II neurons

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Week 5: Variability and Noise in Spike Trains

Estimated Time: ~6 hours

Video Lecture 5: Variability of Spike Trains (96 min)

Part	Topic	Duration	Link
1	Variability of Spike Trains	6 min	Watch
2	Sources of Variability	10 min	Watch
3a	Three Definitions of Rate Code	12 min	Watch
3b	Poisson Model, Survivor Function, and Interval Distribution	15 min	Watch
Math	Poisson Process - A Modern Approach	20 min	Watch
4a	Stochastic Spike Arrival	15 min	Watch
4b	Membrane Potential Fluctuations	13 min	Watch
5	Stochastic Spike Firing in Integrate-and-Fire Models	5 min	Watch

Video Lecture 6: Noise Models (84 min)

Part	Topic	Duration	Link
1	Escape Noise	15 min	Watch
2	Interspike Intervals & Renewal Processes	29 min	Watch
3	Likelihood of a Spike Train	18 min	Watch
4a	Comparison of Noise Models	19 min	Watch
4b	From Diffuse Noise to Escape Noise	7 min	Watch
5	Rate Codes versus Temporal Codes	6 min	Watch

Textbook Reading

• Chapter 7: Variability of Spike Trains and Neural Codes
  • 7.1 Spike Train Variability
  • 7.2 Mean Firing Rate
  • 7.3 Interval Distribution and Coefficient of Variation
  • 7.5 Renewal Statistics
  • 7.6 The Problem of Neural Coding
• Chapter 8: Noisy Input Models
• Chapter 9: Noisy Output - Escape Rate and Soft Threshold

Python Exercise

Week 5 focuses on theoretical concepts (Poisson processes, noise statistics). No dedicated exercise module, but concepts are applied in later exercises.

Key Concepts

• Poisson processes and spike train statistics
• Fano factor and coefficient of variation (CV)
• Rate codes vs temporal codes
• Input noise vs output noise models

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Week 6: Phenomenological Models, GLMs, and Decoding

Estimated Time: ~5 hours

Video Lecture 7: Modern Phenomenological Neuron Models (94 min)

Part	Topic	Duration	Link
1	Models and Data	11 min	Watch
2a	AdEx: Adaptive Exponential Integrate-and-Fire	11 min	Watch
2b	Firing Patterns and Phase Plane Analysis	10 min	Watch
3	Spike Response Model (SRM)	15 min	Watch
4	Generalized Linear Model (GLM)	7 min	Watch
5a	Parameter Estimation	14 min	Watch
5b	Parameter Estimation for Spike Times	7 min	Watch
6	Modeling In Vitro Data	8 min	Watch
7	Helping Humans (BCI applications)	11 min	Watch

Textbook Reading

• Chapter 6: Adaptation and Firing Patterns
  • 6.1 Adaptive Exponential Integrate-and-Fire
  • 6.2 Firing Patterns
  • 6.4 Spike Response Model (SRM)
• Chapter 10: Estimating Parameters of Probabilistic Neuron Models
• Chapter 11: Encoding and Decoding with Stochastic Neuron Models
  • 11.3 Decoding ← Key for BCI applications

Python Exercise

Exercise	Description	Link
AdEx Model	Explore adaptive exponential IF, generate diverse firing patterns (bursting, adapting, delayed), analyze phase plane	Exercise

Key Concepts

• Adaptive exponential integrate-and-fire (AdEx) model
• Generalized Linear Models (GLMs)
• Maximum likelihood parameter estimation
• Neural encoding and decoding for BCIs

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Week 7: Networks and Population Activity

Estimated Time: ~6 hours

Video Lecture 8: Neuronal Populations (85 min)

Part	Topic	Duration	Link
1	Population Activity	9 min	Watch
2	Cortical Populations: Columns and Receptive Fields	7 min	Watch
3	Connectivity - In Cortex and In Models	11 min	Watch
4a	Asynchronous State	13 min	Watch
4b	Mean-Field Argument	10 min	Watch
5	Stationary Mean-Field and Asynchronous State	16 min	Watch
6	Random Networks and Balanced State	21 min	Watch

Video Lecture 9: Fokker-Planck Equation (77 min)

Part	Topic	Duration	Link
1	Integrate-and-Fire Neurons Driven by Stochastic Spike Arrival	6 min	Watch
2	Continuity Equation/Transport Equation	15 min	Watch
3	The Flux of Membrane Potential Trajectories	7 min	Watch
4	Derivation of the Fokker-Planck Equation	16 min	Watch
5	Fokker-Planck Equation with Threshold	15 min	Watch
5B	Quiz on Fokker-Planck Equation	6 min	Watch
6	Random Network of Integrate-and-Fire Neurons	12 min	Watch

Textbook Reading

• Chapter 12: Neuronal Populations
  • 12.1 Columnar Organization
  • 12.2 Identical Neurons: A Mathematical Abstraction
  • 12.3 Connectivity Schemes
  • 12.4 From Microscopic to Macroscopic
• Chapter 13: Continuity Equation and the Fokker-Planck Approach

Python Exercise

Exercise	Description	Link
Brunel Network	Simulate sparse LIF network, explore AI/SR/SI states, vary E/I balance, analyze population dynamics	Exercise

Key Concepts

• Population activity and mean-field theory
• Balanced excitation/inhibition networks
• Asynchronous irregular (AI) state
• Fokker-Planck equation for neuronal populations

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Week 8: Plasticity, Memory, and Decision Making

Estimated Time: ~7 hours

Video Lecture 10: Associative Memory (57 min)

Part	Topic	Duration	Link
1	Introduction: Human Memory and Networks of Neurons	4 min	Watch
2	Classification by Similarity	5 min	Watch
3	Detour: Magnetic Materials	9 min	Watch
4	Hopfield Model	15 min	Watch
5	Learning of Associations	9 min	Watch
6	Storage Capacity	15 min	Watch

Video Lecture 11: Attractor Networks (62 min)

Part	Topic	Duration	Link
1	Attractor Networks	8 min	Watch
2	Stochastic Hopfield Model	18 min	Watch
3	Energy Landscape	14 min	Watch
4	Toward Biology 1: Low-Activity Patterns	6 min	Watch
5	Toward Biology 2: Spiking Neurons	16 min	Watch

Video Lecture 14: Synaptic Plasticity and Learning (85 min)

Part	Topic	Duration	Link
1	Synaptic Plasticity: Motivation and Aims	6 min	Watch
2	Classification of Plasticity	17 min	Watch
3	Model of Short-Term Plasticity	1 min	Watch
3B	Synaptic Short-Term Plasticity (Earlier MOOC)	9 min	Watch
4	Models of Long-Term Plasticity: Hebbian Learning & BCM Rule	17 min	Watch
5	STDP: Spike-Timing Dependent Plasticity	11 min	Watch
6	From Spiking Plasticity Models to Rate Models	9 min	Watch
6b	Math Detour: From Spiking to Rate Models	27 min	Watch
7	Triplet STDP Model	11 min	Watch
8	Online Learning of Memories	15 min	Watch

Textbook Reading

• Chapter 17: Synaptic Plasticity and Learning (Note: Chapter numbering may vary in online version)
• Chapter 19: Decision Making

Python Exercises

Exercise	Description	Link
Hopfield Network	Implement associative memory, store/retrieve patterns, analyze capacity limits, visualize weight matrices	Exercise
Perceptual Decision Making	Simulate competitive attractor dynamics, analyze reaction times, explore decision boundaries	Exercise

Key Concepts

• Hopfield networks and attractor dynamics
• Energy landscape and memory retrieval
• Hebbian learning ("fire together, wire together")
• Spike-timing dependent plasticity (STDP)
• Bienenstock-Cooper-Munro (BCM) rule

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Bonus: Neural Manifolds (Optional Advanced Topic)

Video Lecture 15: Neural Manifolds and Low-Dimensional Dynamics (39 min)

Part	Topic	Duration	Link
1	What are Neural Manifolds?	9 min	Watch
2	Two Views of Neural Activity in the Brain	15 min	Watch
3	Low-Rank Recurrent Neural Networks	15 min	Watch

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Additional Lectures (Decision Making, Perception)

Video Lecture 12: Continuum Models - Cortical Fields and Perception (62 min)

Part	Topic	Duration	Link
1	Aims and Challenges for this Chapter	7 min	Watch
2	Transients	16 min	Watch
3	Spatial Continuum (Cortex)	3 min	Watch
4	Spatial Continuum (Model)	18 min	Watch
5	Solution Types	8 min	Watch
6	Perception	10 min	Watch

Python Exercise: Spatial Working Memory — Simulate ring attractor, explore bump dynamics, model head direction cells

Video Lecture 13: Decision Models - Competitive Dynamics (66 min)

Part	Topic	Duration	Link
1	Introduction: Aims and Challenges of Decision Models	18 min	Watch
2	Perceptual Decision Making	15 min	Watch
3	Theory of Decision Dynamics (Cortex)	11 min	Watch
4	Solutions of Decision Dynamics: Symmetric and Biased Case	8 min	Watch
5	Simulations and Experiments on Decision Dynamics	8 min	Watch
6	Decisions, Actions, Volition	6 min	Watch

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Quick Reference: All Textbook Chapters

Part	Chapter	Link
I. Foundations	1. Introduction	Ch 1
	2. Hodgkin-Huxley Model	Ch 2
	3. Dendrites and Synapses	Ch 3
	4. Phase Plane Analysis	Ch 4
II. Generalized IF	5. Nonlinear IF Models	Ch 5
	6. Adaptation and Firing Patterns	Ch 6
	7. Variability and Neural Codes	Ch 7
	8. Noisy Input Models	Ch 8
	9. Noisy Output: Escape Rate	Ch 9
	10. Estimating Models	Ch 10
	11. Encoding and Decoding	Ch 11
III. Networks	12. Neuronal Populations	Ch 12
	13. Fokker-Planck Approach	Ch 13

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Python Exercises Summary

Install the exercise package:

pip install neurodynex3

Documentation: neuronaldynamics-exercises.readthedocs.io

Complete Exercise List

Week	Exercise	Chapter	Link
1	Leaky Integrate-and-Fire	Ch 1	Exercise
2	Hodgkin-Huxley Model	Ch 2	Exercise
3	Passive Cable	Ch 3	Exercise
4	Phase Plane Analysis	Ch 4	Exercise
4	Type I and Type II Neurons	Ch 4	Exercise
4	Exponential Integrate-and-Fire	Ch 5	Exercise
6	AdEx Model	Ch 6	Exercise
7	Brunel Network (LIF)	Ch 13	Exercise
8	Hopfield Network	Ch 17	Exercise
8	Perceptual Decision Making	Ch 16	Exercise
Bonus	Spatial Working Memory	Ch 18	Exercise

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Last updated: March 2026