Mathematical Sciences: Mathematical Problems Concerning Populations of Oscillators

8901913 科佩尔 这个项目是研究各种问题， 到中央模式发生器（C.P.G.的），这是神经 控制韵律运动刻板方面的网络 活动 这些网络通常涉及振荡子网络 或者细胞与其他振荡器相互作用或者非振荡 神经元 研究最多的CPG之一。的网络是 粗略地配置为振荡器链。 的一个目标 数学是直觉和测试知识的一般 对连通性的各种约束，以便 网络能够正常运行。 目前的努力 在以往成果的基础上，侧重于三个领域：（1） 网络中的远程耦合的作用，（2） 非模振荡网络的构造 子块，但表现得像离散振荡器链， (3)CPG神经活动的相互作用与 它所引导的机械活动。 此外，工作是 就小型无脊椎动物网络引起的问题提出的建议 CPG 's. 这项工作的重点是将 细胞到网络的涌现属性。 各项工作 要与实验人员配合进行。 最后， 提出了一些纯数学的课题。

8901913 Kopell This project is to study a variety of questions relating to central pattern generators (C.P.G.'s), which are neural networks that govern the stereotypic aspects of rhymthmic motor activity. These networks often involve oscillating subnetworks or cells interacting with other oscillators or non-oscillating neurons. One of the most studied C.P.G.'s is a network that is roughly configured as a chain of oscillators. One goal of the mathematics is to intuit and test conjectures about general kinds of constraints on the connectivity, in order that the network be able to function appropriately. The current effort builds on former results and focuses on three areas: (1) the role of long-range coupling in the network, (2) the construction of networks not composed of modular oscillatory subpieces, but behaving like chains of discrete oscillators, (3) the interaction of the neural activity of the C.P.G. with the mechanical activity that it directs. In addition, work is proposed on issues arising from small invertebrate network C.P.G.'s. The focus of that work is to relate properties of the cells to emergent properties of the network. All work is to be done in coordination with experimentalists. Finally, some purely mathematical topics are proposed.