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

• Published in: Physica. D Vol. 455; p. 133887
• Main Authors: Sensi, Mattia, Desroches, Mathieu, Rodrigues, Serafim
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2023; Elsevier
• Subjects: Bifurcation analysis; Canards; Entry–exit function; Mathematics; Slow–fast system; Vesicle cycle; Entry–exit function; Canards; Vesicle cycle; Bifurcation analysis; Slow–fast system
• ISSN: 0167-2789; 1872-8022
• DOI: 10.1016/j.physd.2023.133887

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.