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 gCa = 0 (blue) with gCa > 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 gCa 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.