Multistability of clustered states in a globally inhibitory network

We study a network of m identical excitatory cells projecting excitatory synaptic connections onto a single inhibitory interneuron, which is reciprocally coupled to all excitatory cells through inhibitory synapses possessing short-term synaptic depression. We find that such a network with global inhibition possesses multiple stable activity patterns with distinct periods, characterized by the clustering of the excitatory cells into synchronized sub-populations. We prove the existence and stability of n-cluster solutions in a m-cell network. Using methods of geometric singular perturbation theory, we show that any n-cluster solution must satisfy a set of consistency conditions that can be geometrically derived. We then characterize the basin of attraction of each solution. Although frequency dependent depression is not necessary for multistability, we discuss how it plays a key role in determining network behavior. We find a functional relationship between the level of synaptic depression, the number of clusters and the interspike interval between neurons. This relationship is much less pronounced in the absence of depression. Implications for temporal coding and memory storage are discussed.