  In a network of dynamical systems, concurrent synchronization is a regime
where multiple groups of fully synchronized elements coexist. In the brain,
concurrent synchronization may occur at several scales, with multiple
``rhythms'' interacting and functional assemblies combining neural oscillators
of many different types. Mathematically, stable concurrent synchronization
corresponds to convergence to a flow-invariant linear subspace of the global
state space. We derive a general condition for such convergence to occur
globally and exponentially. We also show that, under mild conditions, global
convergence to a concurrently synchronized regime is preserved under basic
system combinations such as negative feedback or hierarchies, so that stable
concurrently synchronized aggregates of arbitrary size can be constructed.
Robustnesss of stable concurrent synchronization to variations in individual
dynamics is also quantified. Simple applications of these results to classical
questions in systems neuroscience and robotics are discussed.
