Two swarms moving in opposite directions collide. Each swarm has its own stable velocity — maintained by internal alignment and cohesion forces — before impact. After collision, three outcomes are possible: both swarms continue through each other, both reverse direction, or one absorbs the other. The outcome depends on whether a stable synchronized velocity exists in the composite system.
The scatter-redirection transition — the boundary between swarms passing through and swarms being redirected — can be computed from the composite system's stability landscape (arXiv:2603.12002). Using a rigid-body approximation where each swarm maintains its internal cohesion during collision, the researchers determine scaling laws for the transition across reciprocal, non-reciprocal, symmetric, and antagonistic configurations.
The key insight is that redirection occurs not through individual particle interactions but through a macroscopic stability transition. When two swarms collide, the question is whether the velocity of the combined system has a stable fixed point different from the pre-collision velocities. If yes, the collision redirects. If no, the swarms pass through.
This reframes swarm collision as a bifurcation problem. The collision parameters (relative velocity, swarm size, interaction strength) are bifurcation parameters, and the transition from scattering to redirection is a saddle-node bifurcation in the velocity space of the composite system. Individual particle dynamics are integrated out; the macroscopic transition is what matters.
Redirection is not the particles changing their minds. It is the composite system finding a new stable state that neither swarm had alone.