MATHEMATICAL THEORY OF OSCILLATORY NEURAL NETWORKS

振荡神经网络和振荡神经元在 神经系统。然而，神经网络的功能包含了 振荡元素在很大程度上是未被探索的。拟议的工作旨在 开发一套与解决这种关系相关的技术，以及 使用这项技术来加深对某些特殊情况的理解 神经网络。这项工作将集中在一种脊椎动物和一种无脊椎动物上 神经网络，两个中心模式产生器(CPGS)都从事生产 有节奏的马达输出。在每种情况下，这项工作都将与 神经生理学家，他们的数据将限制建模活动。 被研究的脊椎动物CPG是用于波动运动的CPG； 主要实验动物为七鳃鳗。这项工作继续进行着 共同努力制定和调查一项全面而灵活的 可从中得出结论的数学框架 关于七鳗鱼网络如何运作的实验数据。在.工作 不久的将来，我们将重点研究长程耦合的特性 在II个局部振荡要素中，设计 全球涌现行为的局域网络及其相互作用 神经行为和它所调节的机械活动之间的关系。 将设计并开展相关实验。 无脊椎动物CPG是甲壳类口胃神经节(STG)。这 这项工作是一个涉及建模和实验的更大项目的一部分。我们的 该项目的一部分是开发数学来帮助解决这些问题 问题如下：(I)如何解释网络的行为 组成神经元的特性的基础？(Ii)起搏器和 突发振荡模式，这两种模式都是已知存在于STG的， 互动和协作，以产生稳定和灵活的系统行为？

Oscillatory neural networks and oscillatory neurons are common in the nervous system. Yet the function of neural networks that contain OsCillatory elements is largely unexplored. The proposed work aims to develop a body of technique relevant to addressing this relationship, and to use this technique to further the understanding of some particular neural networks. The work will focus on one vertebrate and one invertebrate neural network, both central pattern generators (CPGS) engaged in producing rhythmic motor output. In each case, the work will be collaborative with neurophysiologists whose data will constrain the modelling activities. The vertebrate CPG to be studied is that for undulatory locomotion; the main experimental animal is the lamprey. This work continues a collaborative effort to formulate and investigate a general and flexible mathematical framework within which conclusions may be drawn from experimental data on the lamprey about how the network functions. Work in the immediate future will focus on the properties of long range coupling among the ii local oscillatory elements, the implications of the design of local networks for the global emergent behavior, and the interaction between the neural behavior and the mechanical activity that it regulates. Relevant experiments will be designed and carried out. The invertebrate CPG is the crustacean stomatogastric ganglion (STG). This work is part of a larger project involving modelling and experiments. Our part of the project is to develop mathematics to help address such questions as: (i) How can the behavior of the network be explained on the basis of the properties of the component neurons? (ii) How do pacemaker and emergent modes of oscillation, that are both known to exist in the STG, interact and cooperate to produce stable and flexible system behavior?