Fig. 2: Phase portrait of the resonant spiking system.

The nullclines are shown in black. The non-monotonic “n-shaped" nullcline is critical for spiking behavior. Stable trajectories are shown in solid dark blue. Here both a stable fixed point and stable limit cycle are present. They are separated by an unstable limit cycle approximated as the dashed curve. Light blue arrows are sudden perturbations on input light that take the system off the steady state. Note both positive and negative perturbations can excite the system. The red cross indicates a perturbation timed incorrectly and will not allow the system to move back to rest. However, the perturbation with the green check mark can return the system to rest. Parameters are τ = 0.0625, b = 0.05, a = 0.8, R₁ = 1, η = 1, P_drop = 0.625, ΔV = 0.0625, V_peak = 0.925.