Signal anticipation and delay in excitable media: group delay of the FitzHugh-Nagumo model

TL;DR

This paper derives an expression for the group delay in the FitzHugh-Nagumo model, revealing negative delays at low frequencies that indicate anticipation of slowly fluctuating signals, supported by numerical simulations.

Contribution

It provides a novel analytical expression for group delay in the FitzHugh-Nagumo model and demonstrates signal anticipation effects through numerical analysis.

Findings

Negative group delay occurs at low frequencies.

Slowly fluctuating signals are anticipated by the model.

Numerical simulations support the analytical results.

Abstract

An expression for the group delay of the FitzHugh-Nagumo model in response to low amplitude input is obtained by linearisation of the cubic term of the voltage equation around its stable fixed-point. It is found that a negative group delay exists for low frequencies, indicating that the evolution of slowly fluctuating signals are anticipated by the voltage dynamics. The effects of the group delay for different types of signals are shown numerically for the non-linearised FitzHugh-Nagumo model, and some observations on the signal aspects that are anticipated are stated.