Fij x t xj t j h jxj t hPjostxt

This is called synaptic coupling. Here hj is a sigmoidal function, usually chosen to have maximum value 1, so that cij represents the maximum coupling strength (synaptic conductance). hp°st is typically a linear function (e.g. for Hodgkin Huxley models, hp°st(xi(t)) = Vi(t) — Kij, where Kij is a constant). Some models set h?°st = 1, eliminating the dependence on the post-synaptic neuron, in which case this coupling is called sigmoidal.

If the neurons are connected via a gap junction, then the coupling function is

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