  We consider the problem of characterizing the dynamics of interacting swarms
after they collide and form a stationary center of mass. Modeling efforts have
shown that the collision of near head-on interacting swarms can produce a
variety of post-collision dynamics including coherent milling, coherent
flocking, and scattering behaviors. In particular, recent analysis of the
transient dynamics of two colliding swarms has revealed the existence of a
critical transition whereby the collision results in a combined milling state
about a stationary center of mass. In the present work we show that the
collision dynamics of two swarms that form a milling state transitions from
periodic to chaotic motion as a function of the repulsive force strength and
its length scale. We used two existing methods as well as one new technique:
Karhunen-Loeve decomposition to show the effective modal dimension chaos lives
in, the 0-1 test to identify chaos, and then Constrained Correlation Embedding
to show how each swarm is embedded in the other when both swarms combine to
form a single milling state after collision. We expect our analysis to impact
new swarm experiments which examine the interaction of multiple swarms.
