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IMA Annual Program Year Workshop
Lattice and Nonlocal Dynamical Systems and Applications
December 3-7, 2012

Peter BatesMichigan State University
John Mallet-ParetBrown University
Wenxian ShenAuburn University
Group PhotoOver the past two decades, lattice differential equations and nonlocal evolution equations have been widely studied, both for their interesting mathematical properties and because of the plethora of applications. For instance, one finds long-range interaction in polymeric science, quantum mechanics, neuroscience, genetic regulation, ecology, and image processing. Long-range interactions were included in models formulated by Van der Waals and others, but finding it more convenient to view the range of interaction as infinitesimal, one is lead to PDEs. On the other hand, many systems exhibit genuine long-range spatial and/or temporal interactions and ignoring them results in models poorly matching experimental evidence. Lattice differential equations naturally arise when one discretizes continuum models but they also arise in modeling physically discrete systems, such as interactions on a single strand of DNA, pulses along myelinated neuronal axons, waves in lattice gases, or dispersal or evolution in patchy media or environments, for instance. Since lattice differential equations and nonlocal evolution equations can be cast as infinite-dimensional dynamical systems, this workshop will bring together mathematicians having expertise in different theoretical aspects of this field and scientists with a deeper physical understanding of the applications.

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