871 research outputs found
Coherent Pattern Prediction in Swarms of Delay-Coupled Agents
We consider a general swarm model of self-propelling agents interacting
through a pairwise potential in the presence of noise and communication time
delay. Previous work [Phys. Rev. E 77, 035203(R) (2008)] has shown that a
communication time delay in the swarm induces a pattern bifurcation that
depends on the size of the coupling amplitude. We extend these results by
completely unfolding the bifurcation structure of the mean field approximation.
Our analysis reveals a direct correspondence between the different dynamical
behaviors found in different regions of the coupling-time delay plane with the
different classes of simulated coherent swarm patterns. We derive the
spatio-temporal scales of the swarm structures, and also demonstrate how the
complicated interplay of coupling strength, time delay, noise intensity, and
choice of initial conditions can affect the swarm. In particular, our studies
show that for sufficiently large values of the coupling strength and/or the
time delay, there is a noise intensity threshold that forces a transition of
the swarm from a misaligned state into an aligned state. We show that this
alignment transition exhibits hysteresis when the noise intensity is taken to
be time dependent
The chaotic milling behaviors of interacting swarms after collision
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
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