A62 Loss of synchronization

Topic

An insect swarm can lose the collective synchronization normally maintained among its individuals due to several distinct causes: an increase in environmental noise, a reduction in swarm density that increases the distance between individuals, or external disturbances that shift the movement phase of each individual relative to the others.

The Kuramoto framework explains why any of these three factors can disrupt swarm synchronization: it describes synchronization as a dynamic balance between two forces pulling in opposite directions on each individual's phase. On one hand, the coupling between swarm members tends to align their phases; on the other, the natural spread of individual frequencies—compounded by environmental noise—tends to drive those phases apart.

For the coupling between individuals to prevail in this tug-of-war and keep the swarm synchronized, the coupling strength must exceed a critical threshold that rises alongside environmental noise levels. Consequently, a swarm flying in a noisier environment must maintain higher density than one in a quiet environment; this ensures the effective coupling between individuals reaches the increasingly high threshold demanded by the noise.

When the coupling between swarm members falls below this critical level, synchronization is not lost gradually but collapses relatively quickly: the parameter measuring the swarm's synchronization decays exponentially, and the swarm transitions to a state where individual phases are distributed virtually uniformly, devoid of any recognizable phase coordination. This loss of synchronization has immediate functional consequences for the swarm, depending on the insect involved: the firefly swarm ceases to be visible as a coordinated flashing pattern used to attract mates, while the bee swarm loses the flight coordination that allows it to maintain the cohesive shape in which it normally moves.

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