felice-models/docs-site/docs/neuron_models/fhn/index.md

FitzHugh-Nagumo

Circuit implementing the fhn neuron.

• The circuits in the schematics implement the FHN neuron described.
• 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). The OTA and CMFB are well known designs that can be found in textbooks.

Circuit equation

\begin{align}
    C\frac{dv}{dt} &= I_{app} - I_{passive} - I_{fast} - I_{slow} \\
    \frac{dv_{slow}}{dt} &= \frac{v - v_{slow}}{\tau_{slow}} \\
    \frac{dI_{app}}{dt} &= -\frac{I_{app}}{\tau_{syn}}
\end{align}

where the currents are:

• I_{passive} = g_{max}(v - E_{rev})
• I_{fast} = a_{fast} \tanh(v - v_{off,fast})
• I_{slow} = a_{slow} \tanh(v_{slow} - v_{off,slow})

Examples

See the following interactive notebook for a practical example:

• Basic Usage Example - Introduction to the FitzHugh-Nagumo model