A simple format is disclosed and referred to as Elementary Network Description (END). The format can fully describe a large-scale neuronal model and embodiments of software or hardware engines to simulate such a model efficiently. The architecture of such neuromorphic engines is optimal for high-performance parallel processing of spiking networks with spike-timing dependent plasticity. Methods for managing memory in a processing system are described whereby memory can be allocated among a plurality of elements and rules configured for each element such that the parallel execution of the spiking networks is most optimal.