Propagation of Synfire Activity in Cortical Networks — a Dynamical Systems Approach

Abstract

During the last years, several models and related theories discussed the possible functional role of synchronized neuronal activity in cortical function. Here, we focus on recent findings by Abeles and colleagues on the abundance of accurate spatio-temporal spike patterns in the activity of neurons in the prefrontal cortex of awake behaving monkey, and their dependence on stimulus and behavioral context [1,2]. These findings support the hypothesis, that synchronous spike volleys propagate through the cortex in ‘reverberating synfire chains’ (RSC): feedforward networks with additional feedback connections. Using simulations of simplified, purely feedforward ‘synfire chains’, Diesmann and Gewaltig could demonstrate [3] that the stability of propagation of ‘synfire volleys’ in such chains strongly depends on the density of inter-node connectivity. Thus, the stability properties of these systems are described by iterative maps, which exhibit stable and instable fixpoints for the mean activity and the temporal width of the propagating ‘pulse packet’. Motivated by these results we set out to develop a theoretical analysis of the stability properties of synfire propagations based on dynamical systems theory.