Fig. 2

Formulation of system (1) as the boundary value problem (5)-(8). The first (red) segment is the solution ${\mathbf{u}}_{\mathrm{ON}}(t)$ of (1) with $I_{\mathrm{app}}=20\mu {\text{A/cm}}^2$ and ${\mathbf{u}}_{\mathrm{ON}}(0)$ at the resting potential ${\mathbf{u}}_{\mathrm{OFF}}^{\ast }$, which is an equilibrium of (1) for $I_{\mathrm{app}}=0$ (indicated by the horizontal black dashed line). The total integration time is $T_{\mathrm{ON}}=3\text{ms}$, such that one action potential occurs. The second (blue) segment is the solution ${\mathbf{u}}_{\mathrm{OFF}}(t)$ of (1) with $I_{\mathrm{app}}=0$ and ${\mathbf{u}}_{\mathrm{OFF}}(0)={\mathbf{u}}_{\mathrm{ON}}(1)$; the integration time $T_{\mathrm{OFF}}$ is fixed to a large enough value so that ${\mathbf{u}}_{\mathrm{OFF}}(1)\approx {\mathbf{u}}_{\mathrm{OFF}}^{\ast }$.