On the threshold of excitable systems: An energy-based perspective

Abstract: A fundamental characteristic of excitable systems is their ability to exhibit distinct subthreshold and suprathreshold behaviors. Precisely quantifying this distinction requires a proper definition of the threshold, which has remained elusive in neurodynamics. In this paper, we introduce a novel, energy-based threshold definition for excitable circuits grounded in dissipativity theory, specifically using the classical concept of required supply. According to our definition, the threshold corresponds to a local maximum of the required supply, clearly separating subthreshold passive responses from suprathreshold regenerative spikes. We illustrate and validate the proposed definition through analytical and numerical studies of three canonical systems: a simple RC circuit, the FitzHugh--Nagumo model, and the biophysically detailed Hodgkin--Huxley model.