Mathematical Sciences: Mapping the Dynamics of Neural Network

在这个多学科项目中，伊萨卡学院的研究人员和他的同事古肯海默以及康奈尔大学的其他研究人员专注于口胃神经节的研究。这个由大约30个神经元组成的小神经网络是协调甲壳类动物胃磨和幽门运动的中枢模式发生器。研究人员基于实验测量构建单个神经元的室室模型，并将这些模型合并到子网络模型中。这些系统为开发用于探索动力系统分岔的算法提供了一个试验台。特别注意系统中涉及多个时间尺度的那些方面。该项目的目标是提高对生物系统动态过程的理解，重点是神经系统。研究人员在多学科环境下工作，将实验和数学建模相结合，给予数学和神经科学应有的关注，并确保两者在工作中的任何时候都相互作用。更大的目标是在特定系统的背景下追求的，即研究控制龙虾前肠节律运动的小神经回路。选择这个模型系统是因为它的大小适中，便于实验操作。该项目旨在了解神经系统如何在运动模式之间切换，以及它们如何调节这些模式。

Peck In this multidisciplinary project, the investigator at Ithaca College and his colleagues Guckenheimer and others at Cornell University focus upon studies of the stomatogastric ganglion. This small neural network with approximately 30 neurons is a central pattern generator that coordinates movement of the gastric mill and pylorus of crustacea. The investigators construct compartmental models of individual neurons based upon experimental measurements and amalgamate these into models for subnetworks. These systems provide a testbed for the development of algorithms to explore the bifurcations of dynamical systems. Particular attention is given to those aspects of the systems that involve multiple time scales. The goal of the project is to improve understanding of dynamical processes in biological systems, with an emphasis upon neural systems. The investigators work in a multidisciplinary setting, combining experiment and mathematical modeling, giving due attention to both mathematics and neuroscience, and ensuring that the two interact at all times in the work. The larger goals are pursued in the context of specific systems, namely the study of a small neural circuit that controls rhythmic motions in the foregut of lobsters. This model system has been chosen for its modest size and accessibility for experimental manipulation. The project aims to understand how neural systems switch among motor patterns and how they regulate these patterns.