- A model of a large population of identical excitable neurons with a global slowly decaying inhibitory coupling is studied and its patterns of synchrony are examined. In addition to converging to a homogeneous fixed point and a homogeneous limit cycle, the system exhibits cluster states, in which it breaks spontaneously into a few macroscopically big clusters, each of which is fully synchronized. A method for calculating the stability of cluster states is described and used for investigating the dynamical behavior of the network versus the parameters that describe the neurons and synapses. Effects of stochastic noise on the network dynamics are discussed. At large enough noise the system goes to a globally stationary state. Low levels of noise preserve the cluster-like neuron trajectories. In the regime where a noiseless system converges to a fully synchronized periodic state, relatively low noise levels cause neurons to burst only every two or more consecutive time periods.