Simulating Gamma Waveforms, AM Patterns and 1/f ^α Spectra by Means of Mesoscopic Chaotic Neurodynamics

Abstract

Piecewise linear analysis modeled gamma activity as the output of an adaptive filter with white noise input (Elul 1972). Under this model a point attractor was postulated to govern the dynamics of the olfactory system under noise, which accounted for the broad spectrum of its background activity in the gamma range, the Gaussian amplitude density distribution, and the Rayleigh distribution of the peak amplitudes of the oscillations (Figure 3.13, c, p. 148 in Freeman 1975), but which failed to account for the 1/f^α power spectral density and the spatial patterns of phase cones (Figure I in Prologue, Sections B and C). The gamma burst on inhalation was thought to be governed by a Hopf bifurcation to a limit cycle attractor. The amplitude and frequency modulations of bursts were ascribed to the brief time of access during inhalation, which allowed for an approach to the attractor, but with the next bifurcation coming too quickly to allow the state to settle into a stable orbit.