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，以解决与非线性振子系统及其在生物和工程中的应用有关的问题。参与其中的资深科学家组成了一个专注的、多学科的团队，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。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系统、非线性控制、动物运动、机器人学、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，数学建模继续与实验紧密结合在一起。这个新小组的成立是为了进行三类耦合振子系统的研究：神经、机械和神经机械。每门课的具体问题旨在理解耦合诱导的现象--如同步、能量传递、局部化、谐振模耦合、振荡控制和混沌振荡。此外，具体的问题出现在各种应用中：记忆和学习、链、弦和轴的控制、压缩机、相互作用的气泡、机器人、四足动物运动、鱼的游泳和火蜥蜴的运动。基金将为博士后研究员和研究生提供跨学科研究培训。每年都会举办一系列广为人知的研讨会。最后，将通过一系列技术报告和与行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.