Basic question #5: Can we improve the numerical stability of the Izhikevich model?

Indeed, by decreasing the integration step size from 0.5 ms (Izhikevich default) down to 1/32 ms, the peak of the action potential stabilizes at around ~30 mV, which is the physiologically realistic value:

Only then (with well-behaved action potential amplitudes) is it reasonable to compute the "analog" cross-correlation between two traces:

On the other hand, it occurred to me that I need to think carefully about the scaling of the random input ("thalamic input") as the step size is changed. Presumably, there is a nice theoretic justification for the appropriate scaling. We should also verify that, with correct scaling, the firing rate does not depend (too strongly) on the integration step size.