Slow-fast dynamics in a neurotransmitter release model: delayed response to a time-dependent input signal

TL;DR

This paper generalizes a neurotransmitter release model by increasing its complexity with a degree-four polynomial, analyzing the resulting slow-fast dynamics and transient behaviors through numerical simulations and bifurcation analysis.

Contribution

It introduces a more complex slow-fast system with a higher-degree polynomial and applies advanced analysis techniques to explore its dynamics.

Findings

Identification of transient and asymptotic behaviors

Use of entry-exit function to describe slow dynamics

Numerical bifurcation analysis reveals complex dynamics

Abstract

We propose a generalization of the neurotransmitter release model proposed in \emph{Rodrigues et al. (PNAS, 2016)}. We increase the complexity of the underlying slow-fast system by considering a degree-four polynomial as parametrization of the critical manifold. We focus on the possible transient and asymptotic dynamics, exploiting the so-called entry-exit function to describe slow parts of the dynamics. We provide extensive numerical simulations, complemented by numerical bifurcation analysis.