Dynamics and storage capacity of cortical networks with small-world topology

We study the storage of phase-coded patterns as stable dynamical attractors in recurrent neural networks with small-world topology. The synaptic strength of existent connections is determined by a learning rule based on spike-time-dependent plasticity, with an asymmetric time window depending on the relative timing between preand postsynaptic activity. We store multiple patterns and study the network capacity for fully-connected and sparse networks with different topologies. We study networks where each neuron is connected only to a small number z ≪ N of other neurons, Connections can be short range, between neighboring neurons placed on a regular lattice, or long range, between randomly chosen pairs of neurons. We find that a small fraction of long range connections is able to amplify the capacity of the network. This imply that a small-world-network topology is optimal, as a compromise between the cost of long range connections and the capacity increase.