Initial commit

Co-authored-by: Aradhana Dube <a.dube@rug.nl>
Co-authored-by: Renzo I. Barraza Altamirano <r.i.barraza.altamirano@rug.nl>
Co-authored-by: Paolo Gibertini <p.gibertini@rug.nl>
Co-authored-by: Luca D. Fehlings <l.d.fehlings@rug.nl>

docs-site/docs/neuron_models/wererabbit/index.md

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+# WereRabbit
+
+The wererabbit neuron model is a two coupled oscillator that follows a predator- prey dynamic with a switching in the diagonal of the phaseplane. When the z in equation 1c represents the “moon phase”, when ever it cross that threshold, the rabbit (prey) becomes the predator.
+
+## Circuit equation
+
+$$
+\begin{align}
+    C\frac{du}{dt} &= z I_{bias} - I_{n0} e^{\kappa v / U_t} [z + 26e^{-2} (0.5 - u) z] - I_a \\
+    C\frac{dv}{dt} &= -z I_{bias} + I_{n0} e^{\kappa u / U_t} [z + 26e^{-2} (0.5 - v) z] - I_a \\
+    z &= tanh(\rho (u-v))\\
+    I_a &= \sigma I_{bias} \\
+\end{align}
+$$
+
+| **Parameter** | **Symbol** | **Definition** | **Value** |
+|-----------|--------|------------|-------|
+| Capacitance | C | Circuit capacitance | $0.1\,pF$ |
+| Bias current | $I_{bias}$ | DC bias current for the fixpoint location | $100\,pA$
+Leakage current | $I_{n0}$ | Transistor leakage current | $0.129\,pA$
+Subthreshold slope | $\kappa$ | Transistor subthreshold slope factor | $0.39$
+Thermal voltage | $U_t$ | Thermal voltage at room temperature | $25\,mV$
+Bias scale | $\sigma$ | Scaling factor for the distance between fixpoints | $0.6$
+Steepness | $\rho$ | Tanh steepness for the moonphase | $5$s
+
+## Abstraction
+To simplify the analysis of the model for simulation purposes, we can introduce a dimensionless time variable $\tau=tI_{bias}/C$, transforming the derivate of the equations in $\frac{d}{dt}=\frac{I_{bias}}{C}\frac{d}{d\tau}$. Substituting this time transformation on equation~\ref{eq:wererabbit:circ}
+
+$$
+\begin{equation}
+C\frac{I_{bias}}{C}\frac{du}{d\tau} = z I_{bias} - I_{n0} e^{\kappa v / U_t} [z + 26e^{-2} (0.5 - u) z] - \sigma I_{bias}
+\end{equation}
+$$
+
+And dividing by $I_{bias}$ on both sides:
+
+$$
+\begin{equation}
+    \frac{du}{d\tau} = z - \frac{I_{n0}}{I_{bias}} e^{\kappa v / U_t} [z + 26e^{-2} (0.5 - u) z] - \sigma
+\end{equation}
+$$
+
+Obtaining the following set of equations:
+
+$$
+\begin{align}
+    z &= tanh(\kappa (u-v)) \\
+    \frac{du}{dt} &= z - z \alpha e^{\beta v} [1 + \gamma (0.5 - u)] - \sigma \\
+    \frac{dv}{dt} &= -z - z \alpha e^{\beta u} [1 + \gamma (0.5 - v)] - \sigma
+\end{align}
+$$
+
+| **Parameter** | **Definition** | **Value** |
+|---------------|----------------|-----------|
+| $\tau$ | $tI_{bias}/C$ | -- |
+| $\alpha$ | $I_{n0}/I_{bias}$ | $0.0129$ |
+| $\beta$ | $\kappa/U_t$ | 15.6  |
+| $\gamma$ | -- | $26e^{-2}$ |
+| $\rho$ | Tanh steepness for the moonphase | 5  |
+| $\sigma$ | Scaling factor for the distance between fixpoints | 0.6 |
+
+## Examples
+
+See the following interactive notebook for a practical example:
+
+- [Basic Usage Example](wererabbit.ipynb) - Introduction to the WereRabbit model