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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: