10.4: Properties Controlling Synchronization in Networks of Dynamical Systems
Abstract
This project will develop and apply mathematical and computational approaches to the following significant problems: 1) incoherence-mediated synchronization, 2) coexistence of competing properties governing synchronization, 3) experimental observation of spontaneous symmetry breaking in network synchronization, and 4) stabilization and control of synchronization. To approach these objectives, the PI will analyze the symmetry group associated with the dynamical equations of networked systems to determine solutions (not necessarily stable) of the equations of motion in which nodes have the exact same dynamics regardless of whether they are directly connected or not. As part of this approach, the PI will classify symmetries, identify concurrent changes of the network parameters that preserve the symmetries of the dynamical equations, and expand the existing literature on graph theoretical/spectral theory to characterize the properties of networks exhibiting optimal synchronization properties. The PI will focus on the stability of complete synchronization (i.e., all oscillators synchronized) in networks of diffusively coupled oscillators, for various forms of coupling schemes. Synchronizability will be determined by the eigenvalues of the graph Laplacian matrix. The relevant symmetries that will be investigated are thus the ones that keep the Laplacian, or more generally its eigenvalues, invariant. For concreteness, the PI will first focus on scenarios in which the synchronizability is determined by the smallest nonzero Laplacian eigenvalue which is the case when the master stability function has a single, semi-infinite stability region. The outcomes of the research will be published in peer-reviewed scientific journals.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 12, 2017
- Source ID
- W911NF1510272
Entities
People
- Adilson E. Motter
Organizations
- Army Contracting Command
- Northwestern University
- United States Army