On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs.

ABSTRACT: Point process generalized linear models (PP-GLMs) provide an important statistical framework for modeling spiking activity in single-neurons and neuronal networks. Stochastic stability is essential when sampling from these models, as done in computational neuroscience to analyze statistical properties of neuronal dynamics and in neuro-engineering to implement closed-loop applications. Here we show, however, that despite passing common goodness-of-fit tests, PP-GLMs estimated from data are often unstable, leading to divergent firing rates. The inclusion of absolute refractory periods is not a satisfactory solution since the activity then typically settles into unphysiological rates. To address these issues, we derive a framework for determining the existence and stability of fixed points of

SUBMITTER: Gerhard F 

PROVIDER: S-EPMC5325182 | biostudies-literature | 2017 Feb

REPOSITORIES: biostudies-literature