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28 lines
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Markdown
28 lines
1.0 KiB
Markdown
# FitzHugh-Nagumo
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# Circuit implementing the fhn neuron.
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- The circuits in the schematics implement the FHN neuron described.
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- The FHN neuron is an implementation of the circuit described in (Ribar, L. (2019). Synthesis of neuromorphic circuits with neuromodulatory properties [Apollo - University of Cambridge Repository]. [DOI: 10.17863/CAM.53750](https://doi.org/10.17863/CAM.53750)). The OTA and CMFB are well known designs that can be found in textbooks.
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## Circuit equation
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$$
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\begin{align}
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C\frac{dv}{dt} &= I_{app} - I_{passive} - I_{fast} - I_{slow} \\
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\frac{dv_{slow}}{dt} &= \frac{v - v_{slow}}{\tau_{slow}} \\
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\frac{dI_{app}}{dt} &= -\frac{I_{app}}{\tau_{syn}}
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\end{align}
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$$
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where the currents are:
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- $I_{passive} = g_{max}(v - E_{rev})$
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- $I_{fast} = a_{fast} \tanh(v - v_{off,fast})$
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- $I_{slow} = a_{slow} \tanh(v_{slow} - v_{off,slow})$
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## Examples
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See the following interactive notebook for a practical example:
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- [Basic Usage Example](fhn.ipynb) - Introduction to the FitzHugh-Nagumo model |