Self-sustained dynamics of sparsely connected networks without external noise

Abstract:

There is consensus in the current literature is that stable states of asynchronous irregular firing require (i) very large networks of 10000 or more neurons and (ii) diffuse external background activity or pacemaker neurons. Here, we demonstrate that random networks of integrate and fire neurons with current based synapses assume stable states of self-sustained asynchronous and irregular firing even without external random background (Brunel 2000) or pacemaker neurons (Roudi and Latham 2007). These states can be robustly induced by a brief pulse to a small fraction of the neurons. If another brief pulse is applied to a small fraction of the inhibitory population, the network will return to its silent resting state. We demonstrate states of self-sustained activity in a wide range of network sizes, ranging from as few as 100 neurons to more than 100,000 neurons. Networks previously described (Amit and Brunel 1997, Brunel 2000) operate in the diffusion limit where the synaptic weight is much smaller than the threshold. By contrast, the networks described here operate in a regime where each spike has a big influence on the firing probability of the post-synaptic neuron. In this �combinatorial regime� each neuron exhibits irregular firing patterns, very similar to experimentally observed delay activity.