DynSyst_Special_Topics: Time-varying dynamical networks: theory and applications

Georgia State University Research Foundation, Inc., Atlanta GA

Investigators

Abstract

The research objective of this proposal is to investigate the influence of network structure on the dynamics and the information processing capabilities of networks with a time-varying coupling. This proposal focuses on a largely unexplored area, namely, mathematical analysis and modeling of networks that are composed of dynamical systems, whose coupling structure evolves over time, on a time scale that ranges from fast to slow. The development of the general rigorous theory of dynamical networks with on-off connections and its application to three specific types of engineering, ecological, and neuronal networks constitute the research component of the proposal. The first type is a class of stochastically switched engineering networks, such as power converters, communication and information processing networks with fast on-off connections. The second type of networks is interconnected ecological metapopulations, under the realistic assumption that the migration among the patches is sporadic and due to rare and short term meteorological conditions. The third type of networks is neuronal networks with time-varying connections. Research funded under this grant integrates knowledge from different disciplinary areas in applied mathematics and engineering, including stability and bifurcation theory, graph theory, information theory, ergodic theory and averaging. In many biological, ecological and engineering networks the coupling strength and the connection topology can vary in time. The proposed research applies rigorous mathematical techniques to investigate the interplay between time-varying network structure and overall network dynamics, in view of the time-varying network's use in information processing and its role in synchronization and pattern formation. In particular, the project investigates how the addition of fast switching connections can enhance the performance of networks with static links. The project also addresses the question of vulnerability of networks. Specifically, how well can networks process information when part of the individual systems or links are destroyed, and what advantages do time-varying networks of dynamical systems have over networks with static structure. The results will help to better understand the functioning of realistic networks in nature, as well as give general guidelines for designing information processing networks in engineering. The proposed research integrates research activities into the undergraduate and graduate curriculum through developing an interdisciplinary graduate course in the field of dynamical networks and mentoring undergraduate research projects. The grant directly supports one graduate and two undergraduate students, including those from under-represented groups.