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

We propose a generalization of the neurotransmitter release model proposed in Rodrigues et al. (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. • We extend the neurotransmitter release model from Rodrigues et al. (2016). • We study a planar slow–fast system with a quartic critical manifold using GSPT. • We focus on the delayed response to time-dependent input and asymptotic dynamics. • We find families of canards whose branches exchange position in parameter space. • The exchange depends on the geometry of the quartic critical manifold. [ABSTRACT FROM AUTHOR]