The synfire chain has been proposed as a network model to understand the origin of recurring spatio-temporal spike patterns observed in cortical in-vivo activity . Under transient  or persistent stimulation , synfire chains can form synchronous volleys of spikes ("pulse packets") that stably propagate through the network. We have shown previously  that the spiking dynamics in synfire chains, the existence and stability of asynchronous and synchronous states, can be well understood in the framework of a stationary population-rate model. Here, we demonstrate that both the effect of feedback to an embedding background network and the effect of network heterogeneity (e.g., heterogeneity in the number of inputs per neuron [in-degree]) can be incorporated in this theory. By this means, we show that functionally relevant, i.e., bistable, parameter regimes are mainly determined by rate instabilities and not by the stability of oscillatory modes of the embedding background network . Moreover, this study illustrates that (even stationary) population-rate models can be valuable tools to describe synchronization phenomena on a millisecond time scale. See figure 1.
We acknowledge partial support by the Research Council of Norway (eVITA) and the German Federal Ministry of Education and Research (BMBF grant 01GQ0420. All network simulations were carried out with NEST (see http://www.nest-initiative.org).
Institute of Mathematical Sciences and Technology, Norwegian University of Life Sciences
Theoretical Neuroscience Group, RIKEN Brain Science Institute
Bernstein Center for Computational Neuroscience, Albert-Ludwigs-University