The investigator will develop and apply mathematical and computational methods to predict compensatory, rescue perturbations that can mitigate the propagation of failures in perturbed complex networks. The research is motivated by the increasing availability of information about the component parts of large biological and physical networks, which is creating an unprecedented opportunity to address pressing problems determined by large-scale network dynamics. The project will use nonlinear dynamics and complex network techniques and will be implemented through five complementary components of broad significance: the development of (1) deterministic and (2) stochastic methods to identify rescues; the application of these methods to (3) mitigate extinction cascades in perturbed food-web networks, (4) recover lost cellular function in defective metabolic networks, and (5) control cascading failures in power-grid networks. This research will lead to the identification of physically implementable compensatory perturbations, thereby enabling control of the network's large-scale dynamics. An overarching objective of the project is to integrate underlying principles of this research into the development of teaching and outreach innovations in three different frameworks: (i) summer internship activities for undergraduate students from underrepresented groups; (ii) computer-based interactive tools for undergraduate and graduate complex systems education; and (iii) on-line exhibits in partnership with Chicago's Museum of Science and Industry, which will further integrate the research and educational outcomes of this project.
The proposed mathematical development will create methods that can be used to rescue and control complex networks in a wide range of domains. This will allow the discovery and characterization of new phenomena that are likely to foster breakthroughs in various contexts. In particular, it will enable new ecosystems management approaches to halt the loss of biodiversity, yield new methods to recover lost cellular function, with implications for medical research, and lead to novel methods to mitigate cascading failures in electrical power grids. The planned activities are interdisciplinary and will provide a unique training ground for graduate and undergraduate students (including students from underrepresented groups) in a way that traditional disciplinary research programs cannot. The educational and outreach activities will help create infrastructure for complex systems education at Northwestern and will disseminate the research results and methodologies to a large and diverse audience.
