Simple Person's Applied Mathematics Seminar (SPAMS)
Thursday, February 15, 2018 at 6:00pm to 7:00pm
Room 2-132
SPEAKER: Aden Forrow (MIT)
TITLE: Controlling network dynamics with designed Laplacian spectra
ABSTRACT:
Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such systems, the spectrum of the underlying graph Laplacian plays a key role in controlling the matter or information flow. To complement the traditional procedure of constructing graph ensembles with predefined statistical adjacency characteristics, I will present a mathematically rigorous weighted graph construction that exactly realizes any desired spectrum. I will then illustrate the broad applicability of this approach by showing how gapped spectra can be used to control the dynamics of various archetypal physical systems, in particular inducing chimera states in Kuramoto-type oscillator networks, controlling pattern formation in a generic Swift-Hohenberg model, and causing persistent localization in a discrete Gross-Pitaevskii quantum network. The construction can be generalized to design continuous band gaps through periodic extensions of finite networks.
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