Limits on gating variables

[robertcannon]

Hi Boris,
I saw your note about imposing limits when integrating HH equations with gating variables between 0 and 1.
One useful way round this is a change of variables so that instead of
0 < m < 1, the state variable is x where -inf < x < inf and m = exp(x)/(1+ exp(x)).

Then instead of dm/dt = rf * (1 - m) - rr * m
you have:
dx/dt = (1 + exp(x))^2 / exp(x) * (rf * (1 - m) - rr * m)

This behaves much better with simple integration schemes.

[borismarin]

Thanks @robertcannon !
I wonder which amount of preparsing/optimizations we should apply to expressions in this distilled Lems format; most of my initial experiments involved using a CAS (sympy/symja) to parse math, which allowed for simplifications/facilitated manipulation at the expense of direct correspondence to Lems.
Since I am mostly concerned with fancy libraries for integrating ODEs, it would probably be a good idea to preprocess the dynamics and get the most out of numerical integrators.