Detection of a Dynamical System Attractor from Spike Train Analysis

Abstract

Dynamics of the activity of neuronal networks have been intensively studied from the view point of the nonlinear dynamical system. The neuronal activities are recorded as multivariate time series of the epochs of spike occurrences–the spike trains–which are often effected by intrinsic and measuring noise. The spike trains can be considered as a mixture of a realization of deterministic and stochastic processes. Within this framework we considered several simulated spike trains derived from the Zaslavskii map with additive noise. The ensemble of all preferred firing sequences detected by the pattern grouping algorithm (PGA) in the noisy spike trains form a new time series that retains the dynamics of the original mapping.