  We study the dynamical states that emerge in a small-world network of
recurrently coupled excitable neurons through both numerical and analytical
methods. These dynamics depend in large part on the fraction of long-range
connections or `short-cuts' and the delay in the neuronal interactions.
Persistent activity arises for a small fraction of `short-cuts', while a
transition to failure occurs at a critical value of the `short-cut' density.
The persistent activity consists of multi-stable periodic attractors, the
number of which is at least on the order of the number of neurons in the
network. For long enough delays, network activity at high `short-cut' densities
is shown to exhibit exceedingly long chaotic transients whose failure-times
averaged over many network configurations follow a stretched exponential. We
show how this functional form arises in the ensemble-averaged activity if each
network realization has a characteristic failure-time which is exponentially
distributed.

Neurons and Cognition;Disordered Systems and Neural Networks;Chaotic Dynamics;Biological Physics