Superdiffusive Dispersion and Mixing of Swarms with Reactive Levy Walks

A common swarm task is to disperse evenly through an environment from an initial tightly packed formation. Due to communication and sensing limitations, it is often necessary to execute this task with little or no communication between swarm members. Prior approaches based on repulsive forces or uniform random walks motion, unfortunately, converge slowly or pass through bad transient states before converging. A simple integrate-and-fire mechanism, however, can generate modified Levy flights, thereby producing a near-optimal rapid and monotonic dispersion with no communication. This mechanism also produces rapid mixing of swarms and is a plausibly evolvable generator for the Levy flight behaviors observed in biological organisms.