10.4: Properties Controlling Synchronization in Networks of Dynamical Systems

Project: Research project

Project Details

Description

Recent research in the area of complex networks has significantly increased our understanding of the large-scale structural properties of systems that, like food webs, power grids and the Internet, are composed of many interacting parts. Comparatively less attention has been given to the characterization of dynamical network properties and their relations to structural properties. Collective dynamics manifests itself in many forms in complex networks—bursting neurons, phase-locked power generators, and schooling fish, among others. A number of these processes can be idealized as manifestations of network synchronization, a phenomenon in which different elements of the network keep in pace with each other in a decentralized way.

This project is focused on network synchronization, which is a widespread and broadly significant form of collective dynamics in both natural and engineered systems. Specifically, the project will investigate the still outstanding problems of 1) incoherence-mediated synchronization, 2) competing network structural and dynamical properties governing synchronization, and 3) experimentally observing spontaneous symmetry breaking (chimera states) in the synchronization of homogeneous networks, as well as 4) applications to the stabilization and control of synchronization. The research will be centered on mathematical and computational development, but will include concrete applications to power-grid networks and experiments using networks of mechanical metronomes. The expected outcomes of the project include: (i) establishing rigorous graph-theoretical conditions on the network structure for the emergence of incoherence-mediated synchronization, which has implications for network communication systems; (ii) establishing a mathematical characterization of the interactions between multiple co-existing network and/or oscillator properties in governing the emergence of network synchronization, which can be used to design controls to suppress or enhance synchronization; (iii) implementing an experimental verification of existing theoretical predictions of chimera states in homogeneous networks of identically coupled identical oscillators, thereby addressing a long-standing problem in the field; (iv) identifying numerically and analytically the assignment of tunable parameters that optimize synchronization stability in a realistic representation of the U.S.-South Canada power grid network.

The proposed research promises to strongly impact network systems of interest to the Army, including robotic networks, power grids, biological networks (such as those underlying the circadian system), and social networks. The research on synchronization has the potential to impact communication systems and wireless networks of moving agents. The proposed applications to the control and stabilization of synchronous states will address a well-recognized Army need for perturbation-resilient infrastructure/physical networks, and contribute to the development of self-healing smart networks.

The project is inherently interdisciplinary and will involve collaborations between the PI (a physicist) and co-PI (a mathematician)—both with have extensive expertise in network synchronization. The project will also involve a full-time postdoctoral researcher, to whom this research will provide a unique interdisciplinary training opportunity, thus contributing to the formation of the next generation of interdisciplinary scientists. The tradition of Northwestern University in dynamics, control, and network research, as well as the affiliatio
StatusFinished
Effective start/end date8/1/155/31/19

Funding

  • Army Research Office (W911NF-15-1-0272-P00003)

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