Mathematical Sciences/GIG: Applied Mathemaatics for Systems of Oscillators in Biology and Engineering

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PROJECT SUMMARY This award will establish the infrastructure of a new interdisciplinary group to tackle questions concerning systems of nonlinear oscillators and their applications in biology and engineering. The senior scientists involved form a focused, multi-disciplinary team consisting of applied mathematicians, neuroscientists, biomedical engineers, and mechanical engineers. Each team member has extensive experience studying systems of coupled oscillators, with fields of expertise including nonlinear dynamical systems, nonlinear control, animal locomotion, robotics, fluid mechanics, neurophysiological oscillators, circuit models, asymptotic analysis, and partial differential equations. Moreover, the mathematical modeling continues to be closely intertwined with experiments. This new group was formed to conduct research in three classes of coupled oscillator systems: neural, mechanical, and neuro-mechanical. The specific questions addressed for each class aim at understanding coupling-induced phenomena-such as synchronization, energy transfer, localization, resonant mode coupling, oscillatory control, and chaotic oscillations. In addition, the specific problems arise in a variety of applications: memory and learning, control of chains, strings and shafts, compressors, interacting gas bubbles, robotics, quadruped motion, fish swimming, and salamander locomotion. Funds will provide training in interdisciplinary research for postdoctoral fellows and graduate students. A well-publicized seminar series will occur each year. Finally, technology transfer will be fostered by a technical report series and direct discussion with industrial collaborators.