Research Projects

Diffusively Coupled Networks: Synchronization, De-Synchronization and Structure

Murat Arcak

National Science Foundation ECCS 1101876

This project is developing novel design and analysis techniques for spatially distributed networks that exhibit a diffusive coupling structure, in which the feedback is a local sum of differentials of variables with respect to neighbors. This form of coupling encompasses feedback laws for coordination of multi-agent systems, electromechanical coupling of synchronous machines in power systems, and local update laws in distributed agreement algorithms, among other examples. In contrast to the homogenizing effect often attributed to diffusion, diffusively coupled networks exhibit surprisingly rich spatial phenomena. The objective of the project is to unravel structural properties of agent dynamics and their interconnection that yield prescribed spatial behaviors. With a system-theoretic understanding of these properties, we pursue design tools that either enhance homogeneous behavior (e.g., for synchronization of physiological processes and oscillator circuits) or induce desirable forms of inhomogeneity (e.g., for programmed pattern formation).