  Synaptic, dendritic and single-cell kinetics generate significant time delays
that shape the dynamics of large networks of spiking neurons. Previous work has
shown that such effective delays can be taken into account with a rate model
through the addition of an explicit, fixed delay [Roxin et al. PRL 238103
(2005)]. Here we extend this work to account for arbitrary symmetric patterns
of synaptic connectivity and generic nonlinear transfer functions.
Specifically, we conduct a weakly nonlinear analysis of the dynamical states
arising via primary instabilities of the asynchronous state. In this way we
determine analytically how the nature and stability of these states depend on
the choice of transfer function and connectivity. We arrive at two general
observations of physiological relevance that could not be explained in previous
works. These are: 1 - Fast oscillations are always supercritical for realistic
transfer functions. 2 - Traveling waves are preferred over standing waves given
plausible patterns of local connectivity. We finally demonstrate that these
results show a good agreement with those obtained performing numerical
simulations of a network of Hodgkin-Huxley neurons.
