Spiking neuron model II | Theory of Hybrid Systems

Model description

The general dynamics of the model of spiking neurons is defined by the following ODE.

$\left\{ \begin{array}{rcl} C\cdot \dot{v} & = & k\cdot (v - v_r) \cdot (v - v_t) - u + I \\ \dot{u} & = & a\cdot (b\cdot (v - v_r) - u) \end{array} \right.$

wherein the constant parameters are given by $C = 100$ , $v_r = -56$ , $v_t = -42$ , $I = 300$ , $a = 0.03$ , $b = 8$ and $k = 1$ . The values of $v$ , $u$ are reset to $-53 + 0.04\cdot u$ and $u + 20$ respectively when $v \geq 40 - 0.1\cdot u$ .