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Automatic calculation of resting state #1064

@romainbrette

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@romainbrette

I think we discussed that at some point, but can't remember the discussion. It would be nice to have a way to automatically calculate the resting state of a model, ie, X such that f(X)=0, where dX/dt=f(X). This would be particularly useful for HH-type equations, and for model fitting.

A trivial idea is simply to run the model with a large dt. A better idea is to use a root finding algorithm, which would conceptually amount to running the model with a different state updater. For example, the secant method. The only technical difficulty here is that the method uses the previous two time steps. This could be solved for example by duplicating the variables, and having the state updater make a copy of one set to the other. Alternatively, we use any gradient-free method from scipy.optimize, with the function f (that might actually be simpler).

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