  There is consensus in the current literature that stable states of
asynchronous irregular spiking activity require (i) large networks of 10 000 or
more neurons and (ii) external background activity or pacemaker neurons. Yet
already in 1963, Griffith showed that networks of simple threshold elements can
be persistently active at intermediate rates. Here, we extend Griffith's work
and demonstrate that sparse networks of integrate-and-fire neurons assume
stable states of self-sustained asynchronous and irregular firing without
external input or pacemaker neurons. These states can be robustly induced by a
brief pulse to a small fraction of the neurons, or by short a period of
irregular input, and last for several minutes. Self-sustained activity states
emerge when a small fraction of the synapses is strong enough to significantly
influence the firing probability of a neuron, consistent with the recently
proposed long-tailed distribution of synaptic weights. During self-sustained
activity, each neuron exhibits highly irregular firing patterns, similar to
experimentally observed activity. Moreover, the interspike interval
distribution reveals that neurons switch between discrete states of high and
low firing rates. We find that self-sustained activity states can exist even in
small networks of only a thousand neurons. We investigated networks up to 100
000 neurons. Finally, we discuss the implications of self-sustained activity
for learning, memory and signal propagation.
