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

该奖项将建立一个新的跨学科小组的基础设施，以解决有关非线性振荡器系统及其在生物学和工程中的应用的问题。参与的资深科学家组成了一个由应用数学家、神经科学家、生物医学工程师和机械工程师组成的专注的多学科团队。每个团队成员都有研究耦合振荡器系统的丰富经验，其专业领域包括非线性动力学系统，非线性控制，动物运动，机器人，流体力学，神经生理振荡器，电路模型，渐近分析和偏微分方程。此外，数学模型继续与实验紧密交织在一起。这个新小组的成立是为了研究三类耦合振荡器系统：神经、机械和神经-机械。每节课的具体问题旨在理解耦合引起的现象，如同步、能量转移、局部化、共振模式耦合、振荡控制和混沌振荡。此外，在各种应用中出现的具体问题：记忆和学习，链，串和轴的控制，压缩机，相互作用的气泡，机器人，四足运动，鱼类游泳和蝾螈运动。基金将为博士后和研究生提供跨学科研究培训。每年将举行一次广为宣传的系列研讨会。最后，将通过一系列技术报告和与工业合作者的直接讨论来促进技术转让。

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.