FitzHugh-Nagumo excitable neuron

What you are seeing: a two-variable reduction of the Hodgkin-Huxley neuron model: $\dot v = v - v^3/3 - w + I$, $\dot w = \epsilon (v + a - b w)$ with $a = 0.7$, $b = 0.8$, $\epsilon = 0.08$. The fast variable $v$ is voltage, the slow variable $w$ is recovery. External input $I$ tunes the system from excitable rest (one spike per suprathreshold kick) to limit-cycle oscillation.

Press kick to jump $v$ to 0 from rest. If the kick is subthreshold (small), $v$ returns to rest. If suprathreshold (large enough $I$ or $v$ jump), the system fires one full action potential before returning. Slide $I$ above 0.4 and the system goes through a Hopf bifurcation into periodic firing. The phase portrait shows the trajectory relative to the cubic nullcline.