Iterative theoretical predictions for QIF model with spike waveform: stable and unstable 1-spike limit cycles.

(A) f-I curves for QIF model with spike waveform, each panel comparing g_Ca = 0 (blue) with g_Ca > 0 as indicated (color), as well as the theoretical predictions (black). The iterative theory produces a sequence of ISIs, the final 20 are plotted as 1/ISI at each bias (black dots), and their average value versus bias is superimposed (solid black). (B) For the highest g_Ca value, ISI return maps are shown for six illustrative bias current values starting with a low bias stable 1-spk limit cycle (top left panel), through bifurcations to aperiodic spiking, with windows of repeating sequences, and back to stable 1-spk limit cycles at high biases (bottom right panel). The same 20 ISIs from A are also plotted in B. It can be seen that at μ = 20.5, a stable sequence of 3 intervals repeats. Similarly, the bottom left panel shows similar sequence of 3 ISIs almost repeats, but 2+ slightly different versions of it repeat, illustrating how regions with stable N-spike ISI sequences transition to other regions with stable M-spike ISI sequences.