Izhikevich Neuron Model

The Diversity of Firing

The Izhikevich model is a powerful “phenomenological” model. It doesn’t aim to simulate every ion channel; instead, it uses a simplified system of two differential equations to replicate the behavior of almost any known cortical neuron.

The Dynamics

The model is defined by: \(v' = 0.04v^2 + 5v + 140 - u + I\) \(u' = a(bv - u)\)

Where $v$ represents the membrane potential and $u$ is a recovery variable providing negative feedback.

Implementation Highlights

• Parameter Mapping: I implemented a library of 20 distinct neuron types (Regular Spiking, Fast Spiking, Chattering, etc.) based on the original 2003/2004 papers.
• Phase Plane Analysis: My simulation includes a visualisation of the $v-u$ phase plane, allowing users to see how nullclines and fixed points shift to create different spiking regimes.
• Interactive Selector: Using Pluto.jl, visitors can toggle between neuron types to instantly see changes in the spike train.

Why it Matters

This model bridges the gap between the biorealistic (Hodgkin-Huxley) and the abstract (LIF). It’s the gold standard for large-scale simulations that require biological variety without the immense computational cost of conductance-based models.

Note

This model was created using Google Gemini 3 to focus on learning and understanding the fundamentals of the Izhikevich model, rather than the implementation details.

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🤝 Let’s Connect

Are you working on neural modeling or systems neuroscience? I am always looking for opportunities to collaborate or contribute to computational research. Feel free to reach out via LinkedIn or Email.