The piriform cortex is rich in recurrent excitatory synaptic connections between pyramidal neurons. We asked how such connections could shape cortical re- sponses to olfactory lateral olfactory tract (LOT) inputs. For this, we constructed a computational network model of anterior piriform cortex with 2000 multicompartment, multiconductance neurons (500 semilunar, 1000 layer 2 and 500 layer 3 pyramids; 200 superficial interneurons of two types; 500 deep interneurons of three types; 500 LOT afferents), incorporating published and unpublished data. With a given distribution of LOT firing patterns, and increasing the strength of recurrent excitation, a small number of firing patterns were observed in pyramidal cell networks: first, sparse firings; then temporally and spatially concentrated epochs of action potentials, wherein each neuron fires one or two spikes; then more synchro- nized events, associated with bursts of action potentials in some pyramidal neurons. We suggest that one function of anterior piriform cortex is to transform ongoing streams of input spikes into temporally focused spike patterns, called here “cell assemblies”, that are salient for downstream projection areas.