Transition between weak-noise-induced resonance phenomena in a slow-fast neural dynamical system

Marius Yamakou

Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

Abstract: We consider a singularly perturbed stochastic nonlinear dynamical system derived from neuroscience. For this system, we will independently uncover the mechanisms that underlie two different forms of weak-noise-induced resonance phenomena, namely, self-induced
stochastic resonance (SISR) and inverse stochastic resonance (ISR). We will then show that SISR and ISR are in fact mathematically related through the relative geometric positioning (and stability) of the fixed point and the generic folded singularity of the critical manifold of the system. This result could explain the experimental observation where real biological neurons with identical physiological features and synaptic input are found to sometime encode different information.