ModelingNeuralDynamics

An Introduction to Modeling Neuronal Dynamics - Christoph Borgers in python

PING gamma rhythm  ·  gamma coherence  ·  PING network with STDP

Installation

The shared helper package used by some chapters is on PyPI:

pip install modelingneuraldynamics

What's supported

Chapters are ported from the book's original MATLAB programs to Python. Every tracked chapter is now a single, tested chapterNN.ipynb notebook that installs its own dependencies and opens directly in Colab.

• 38 / 38 tracked chapters converted to notebooks (✅)
• Chapters 2 and 6 have no Python example in the book.

Full chapter-by-chapter status (click to expand)

#	Chapter	Status	Open
1	Modeling a Single Neuron	✅ Notebook	guide
3	The Classical HH ODEs	✅ Notebook	guide
4	Numerical Solution of HH ODEs	✅ Notebook	guide
5	The Simple Model of Neurons in Rodent Brains	✅ Notebook	guide
7	Linear Integrate-and-Fire (LIF) Neurons	✅ Notebook	guide
8	Quadratic Integrate-and-Fire (QIF) and Theta Neurons	✅ Notebook	guide
9	Spike Frequency Adaptation	✅ Notebook	guide
10	The Slow-Fast Phase Plane	✅ Notebook	guide
11	The Saddle-Node Bifurcation	✅ Notebook	guide
12	Two-Dimensional Bifurcation Analysis	✅ Notebook	guide
13	Hopf Bifurcations	✅ Notebook	guide
14	Model Neurons of Bifurcation Type 2	✅ Notebook	guide
15	Canard Explosions	✅ Notebook	guide
16	Model Neurons of Bifurcation Type 3	✅ Notebook	guide
17	Frequency-Current Curves	✅ Notebook	guide
18	Bistability Resulting from Rebound Firing	✅ Notebook	guide
19	Bursting	✅ Notebook	guide
20	Chemical Synapses	✅ Notebook	guide
21	Gap Junctions	✅ Notebook	guide
22	A Wilson-Cowan Model of an Oscillatory E-I Network	✅ Notebook	guide
23	Entrainment by Excitatory Input Pulses	✅ Notebook	guide
24	Synchronization by Fast Recurrent Excitation	✅ Notebook	guide
25	Phase Response Curves (PRCs)	✅ Notebook	guide
26	Phase Locking of Two Oscillators	✅ Notebook	guide
27	Phase Locking with Delays	✅ Notebook	guide
28	Weakly Coupled Oscillators	✅ Notebook	guide
29	Stability of the Synchronous State	✅ Notebook	guide
30	The PING Model of Gamma Rhythms	✅ Notebook	guide
31	ING Rhythms	✅ Notebook	guide
32	M-Current PING and Poisson PING	✅ Notebook	guide
33	M-Current PING and PINB	✅ Notebook	guide
34	Nested Gamma-Theta Rhythms	✅ Notebook	guide
35	Periodic Inhibition	✅ Notebook	guide
36	F-I Curves: Pulsed Excitation	✅ Notebook	guide
37	Thresholding in PING	✅ Notebook	guide
38	Gamma Coherence	✅ Notebook	guide
39	Short-Term Depression and Facilitation	✅ Notebook	guide
40	Spike-Timing-Dependent Plasticity (STDP)	✅ Notebook	guide

Running brian/ chapters on Colab

brian/ holds a separate, Brian2-based implementation, one notebook per chapter. Every notebook there can also be opened directly in Google Colab — click a chapter's badge below.

Chapter	Colab
01 - Modeling a Single Neuron
04 - Numerical Solution of HH ODEs
05 - Three Simple Models of Neurons in Rodent Brains
07 - Linear Integrate and Fire (LIF) Neurons
08 - Quadratic Integrate and Fire (QIF) and Theta Neurons
09 - Spike Frequency Adaptation
20 - Chemical Synapses

Introduction

This book is intended as a text for a one-semester course on Mathematical and Computational Neuroscience for upper-level undergraduate and beginning graduate students of mathematics, the natural sciences, engineering, or computer science. An undergraduate introduction to differential equations is more than enough mathematical background. Only a slim, high school-level background in physics is assumed, and none in biology.

Topics include models of individual nerve cells and their dynamics, models of networks of neurons coupled by synapses and gap junctions, origins and functions of population rhythms in neuronal networks, and models of synaptic plasticity.

An extensive online collection of Matlab programs generating the figures accompanies the book.

matlab code gathered from here

Python codes provided by contributors

See the practical Python chapter guides for the concepts, equations, example map, and expected results for every implemented chapter.