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. The software and hardware engines are optimized to take into account short-term and long-term synaptic plasticity in the form of LTD, LTP, and STDP.