Abstract
Abstract In this work, we revisit two traditional models of action potential generation in excitable cells, the Hodgkin-Huxley (HH) and the FitzHugh-Nagumo (FHN) models. The main goal is to evaluate the possibility of modeling the generation of the action potential via a single delay-differential equation (DDE). Delay-differential equations are important mathematical tools and can reproduce a great diversity of biological phenomena. However, their use in modeling of action potentials is still incipient. In this paper, we present new models based on single delay-differential equation. The solutions of the new models are similar to those of the original HH and FHN models. Based on these results, we claim that delay-differential equations can also be used as building blocks in the development of models of cell electrophysiology.
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