Statistical fluctuations of activity in localized neural populations

Abstract

A model for the activity of localized neural populations consisting of coupled excitatory and inhibitory subpopulations (Wilson & Cowan, 1972) is generalized in order to include the effects of statistical fluctuations. By adding Gaussian delta-correlated noise to the deterministic equation of motion a Fokker-Planck process is obtained.For appropriate changes of the external inputs (afferent excitation or inhibition) two different types of transitions between the unexcited and excited states of a subpopulation are discussed. 1. (i) The excitatory activity shows a discontinuous transition (comparable to a first order phase transition). The decay time of metastable states (hysteresis) and a “critical slowing down” of fluctuations are calculated. 2. (ii) The inhibitory activity exhibits a smooth almost linear transition. Inside the broad transition region the activity is more localized around its mean value than outside as long as the fluctuations are small and the coupling of the excitatory activity is negligible.For strong coupling the localization as well as some “speeding up” of fluctuations are destroyed.