Stable Concurrent Synchronization in Dynamic System Networks

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  • 27 October 2005
Abstract
In a network of connected dynamical systems, concurrent synchronization is a regime where multiple groups of fully synchronized elements coexist. Such a regime corresponds to a flow-invariant linear subspace of the global state space. We present a sufficient condition for a general dynamical system to globally converge to such a subspace, thus providing a systematic theoretical tool to study concurrent synchronization in dynamic system networks. 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. Simple applications of these results to classical questions in systems neuroscience and robotics are discussed.

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