The sensitivity function of excitable feedback systems

The sensitivity function S(s) = 1/(1 + L(s)) is a central concept of feedback theory, defined from the loop gain (or return ratio) L(s). Ever since the pioneering work of Hodgkin and Huxley, excitable neurons have been experimentally characterized by a voltage dependent loop gain L(s;V). We propose that the loop gain L(s;V ) of excitable models have an organizing center, that is, a distinguished point in the parameter and voltage spaces that organizes the sensitivity of the feedback system into a discrete set of qualitatively distinct behaviors. The concept is directly borrowed from singularity theory. It suggests an appealing meeting point between LTI control theory and dynamical systems theory for the analysis of nonlinear feedback systems.