Izhikevich Model

The Izhikevich model is a simple yet biologically plausible model of neuronal spiking dynamics. It is given by the equations:

\[ \frac{dv}{dt} = 0.04v^2 + 5v + 140 - u + I \] \[ \frac{du}{dt} = a(bv - u) \]

with a reset condition:

\[ \text{if } v \geq 30, \text{ then } v \leftarrow c, \quad u \leftarrow u + d \]