Weak stochastic perturbation of a multiple-time scale nonlinear oscillator and resonance phenomena

Abstract:

In this talk, we delve into the dynamics of a stochastic multiple-timescale nonlinear oscillator, serving as a model for biological neurons. Leveraging the tools of large deviation theory and stochastic sensitivity analysis, we unveil the underlying mechanisms governing two intriguing noise-induced resonance phenomena: self-induced stochastic resonance (SISR) and inverse stochastic resonance (ISR).
While previous research has predominantly emphasized the harmonizing effects of noise and heterogeneity on coupled oscillator dynamics, mainly concluding that introducing optimal heterogeneity alongside noise consistently amplifies resonance mechanisms like stochastic resonance and coherence resonance induced solely by noise, this talk challenges the prevailing consensus.
Through mean-field analysis, we demonstrate that the impact of heterogeneity on SISR can only be antagonistic. Furthermore, we show that, in the weak noise limit, SISR and ISR are intricately connected through the relative geometric positioning and stability of the fixed point and the generic folded singularity on the critical manifold of the oscillator. This mathematical insight could shed light on experimental observations wherein neurons with identical morphological features occasionally encode distinct information despite receiving identical synaptic input.