Some results on noise-induced resonance phenomena in neuronal dynamics, mathematical difficulties, and machine learning applications.

This talk focuses on the effects of noise and heterogeneity (diversity) on neuronal dynamics, with a particular emphasis on self-induced stochastic resonance (SISR). The previous literature has analyzed the combined effects of noise and diversity in neural dynamics and mainly concluded that adding optimal diversity on top of noise will further enhance resonance phenomena (including stochastic resonance, coherence resonance, and even synchronization) caused by noise alone, i.e., the role of optimal diversity is always constructive. The first part of the talk challenges this conclusion by demonstrating that the effect of diversity on self-induced stochastic resonance can only be antagonistic. The second part of the talk discusses the mathematical difficulties of analyzing SISR in n-dimensional (n>2) dynamical systems without a slow-fast structure; in particular, we shall discuss this using the Hodgin-Huxley neuron model. Finally, if time allows, we shall briefly discuss potential applications of noise-induced resonance phenomena in enhancing bio-inspired machine learning based on reservoir computing.