We define the “Pulse Synchronization” problem that requires nodes to achieve tight synchronization of regular pulse events, in the settings of distributed computing systems. Pulse-coupled synchronization is a phenomenon displayed by a large variety of biological systems, typically overcoming a high level of noise. Inspired by such biological models, a robust and self-stabilizing pulse synchronization algorithm for distributed computer systems is presented. The algorithm attains near optimal synchronization tightness while tolerating up to a third of the nodes exhibiting Byzantine behavior concurrently. We propose that pulse synchronization algorithms can be suitable for a variety of distributed tasks that require tight synchronization but which can tolerate a bound variation in the regularity of the synchronized pulse invocations.