Habilitations-Vorstellungsvortrag: Marius Yamakou: Weak Stochastic Perturbations of a Multiple Timescale Dynamical System: Insights into Self-Induced Stochastic Resonance

Abstract: How do biological neurons use stochastic noise to encode information deterministically? This talk considers a stochastic multiple-timescale dynamical system with a strong timescale separation modeling a biological neuron in the excitable state, i.e., where the zero-noise dynamics do not display a limit cycle nor even its precursor. Within the frameworks of Geometric Singular Perturbation Theory and Large Deviation Theory, I will establish, with high precision, the asymptotic matching conditions and locations under which and where a stochastic phase trajectory almost surely escapes from the normally hyperbolic parts of the critical manifold periodically, thereby inducing a limit cycle solution that is absent without noise. The analysis unveils a nuanced mechanism in neuroscience known as self-induced stochastic resonance, where stochastic noise is pivotal in optimizing the periodic processing of information within the neuron, revealing an intricate interplay between determinism and stochasticity.