Synchronization in networks of mobile oscillators

Synchronization is one of the paradigmatic
examples of emergence of collective behaviors in populations of
oscillating units,
depending not only on the type of individual dynamics but on the
pattern of interactions.
In nature there are many examples of synchronization where the
connections between the units are not fixed
in time. Here we present a model of synchronization of oscillators that
move on a 2-d plane interacting only
with other oscillators that are within a finite range.
This makes that the network of interactions changes in time.
We show that there exists an optimal regime
where both fast synchronization and high efficiency are achieved.
We propose an analytical framework based on the
set of linearized equations with time dependent interactions that can be
applied to any type of agent motion and oscillator dynamics.
This approach enables to estimate the asymptotic behaviors of the
system.