Noise-Induced Precursors of State Transitions in the Stochastic Wilson–Cowan Model

• DOI: 10.1186/s13408-015-0021-x
• Publication Date: 2016-01-11T21:30:47Z
• Authors: Ehsan Negahbani; D. Alistair Steyn...; Moira L. Steyn-Ross; Marcus T. Wilson; Jamie W. Sleigh
• Keywords: 0303 health sciences; 03 medical and health sciences; Research

The Wilson-Cowan neural field equations describe the dynamical behavior of a 1-D continuum excitatory and inhibitory cortical aggregates, using pair coupled integro-differential equations. Here we use bifurcation theory small-noise linear stochastics to study range phase transitions-sudden qualitative changes in state system emerging from bifurcation-accessible network. Specifically, examine saddle-node, Hopf, Turing, Turing-Hopf instabilities. We introduce stochasticity by adding small-amplitude spatio-temporal white noise, analyze resulting subthreshold fluctuations an Ornstein-Uhlenbeck linearization. This analysis predicts divergent correlation spectral characteristics activity during close approach below. validate these theoretical predictions numerical simulations. results demonstrate role noise emergence critically slowed precursors both space time, suggest that early-warning signals are universal feature bifurcation. In particular, precursor likely have neurobiological significance as early warnings impending change cortex. support this claim with vitro local potentials recorded slices mouse-brain tissue. show period leading up spontaneous seizure-like events, mouse characteristic focusing toward lower frequencies concomitant growth fluctuation variance, consistent critical slowing near point. observation biological criticality has clear implications regarding feasibility seizure prediction.