A Structurally-Based Approach to Nonlinear Analysis and Design of Networks

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Objective:The dynamic behavior of various natural and technological networks is dictated by the structure of interactions between the components rather than by detailed properties of the components. This project will develop a new approach that exploits the network structure while broadly characterizing the components by their essential properties, such as passivity and time scales, that are relevant to the ensemble behavior. This structurally based approach will bridge the gap between nonlinear systems techniques and high order, complex network models. The search for important network structures will be guided by biochemical reaction networks which have evolved into several efficient circuit patterns in gene regulation, cell signaling, and biosynthetic pathways.Intellectual Merit:The first part of this project will pursue a passivity based approach to biochemical reaction networks that encompass and significantly strengthen an existing stability criterion in mathematical biology for cyclic interconnection structures. Because passivity is at the core of this stability criterion, we will be able to obtain generalized criteria for other network topologies, such as branched pathways in metabolic networks. The next research topic is verification of passivity properties in network models and modification of the proposed stability criteria to account for time delays. The final topic is the use of passivity properties to ensure robustness against diffusive instabilities in spatially distributed models. The second part of the project will develop a novel model reduction technique that exploits a clustered structure inherent in numerous biological and engineering networks. This technique relies on a timescale separation induced by the structure rather than by the specific parameters of the network, and is particularly promising for order reduction of Markov chains.Broader Impacts:The PI will introduce an undergraduate level course entitled Nonlinear Phenomena in Engineering and Biology¡± and a graduate level course entitled Networks of Dynamic Systems, both of which will be highly interdisciplinary and research oriented. He will continue to recruit graduate students from underrepresented groups and to work with high school students in the New Visions Program a joint research and education program of Rensselaer Polytechnic Institute and local school districts that aims to attract talented students to careers in science and technology.