This is a toy which lets you observe the response of Izhikevich model neurons in response to different input currents and parameters. The model tracks two state variables (the membrane potential $v$ and a recovery variable $u$) which evolve according to the following coupled ODEs:
$$\begin{aligned} \frac{dv}{dt} &= 0.04\,v^2 + 5v + 140 - u + I \\ \frac{du}{dt} &= a\,(b v - u) \end{aligned}$$These equations pair with two discrete rules for resetting after a spike: whenever $v$ reaches $30$, it gets reset to $c$, and $u$ is bumped by $d$. $a$ and $b$ describe the timescale and sensitivity of the recovery variable, and thus govern the spiking behavior.
Below is a window which time-integrates these equations. You can adjust the parameters to gain an intuition for different model neurn regimes, or select a preset for a canonical cell type. See Izhikevich's paper, “Simple Model of Spiking Neurons” (pdf), for the source of these dynamics.
input current