Mathematical Sciences: Dynamic Bifurcation Phenomena in Excitable Systems

数学科学：可激励系统中的动态分岔现象

• 批准号: 9107538
• 负责人: Steven Baer
• 金额: $ 7.08万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-08-01 至 1995-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9107538&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Dynamic; Bifurcation; Phenomena

The modeling and analysis of dynamic bifurcation phenomena is important in science and engineering because experiments are often performed by dynamically tuning one or more parameters until destabilization causes a transition to a new observed state or behavior. Using numerical and computational methods, this project will investigate accommodation phenomena in spatially-unrestricted axons and myelinated nerve segments. A primary goal is to establish the interrelationship between passive loading (both conductive and capacitive) and accommodation in nerve cells and how it affects signaling. The project requires computational and analytic bifurcation studies of reaction-diffusion equations with slowly varying boundary and interface conditions. Another objective is to classify and explore how different kinds of random fluctuations influence accommodation in nerve models. Stochastic perturbation methods for exit time estimates and numerical simulations will be employed. In neuroscience, threshold and accommodation experiments at the cellular level are performed by slowly depolarizing an excitable membrane by ramping or stepping up an applied current. Such experiments to investigate accommodation phenomena in spatially-unrestricted axons and myelinated nerve segments are important for understanding why and how conduction failures occur in partially demyelinated nerve; debilitating diseases such as Multiple Sclerosis can induce lesions that partially demyelinate the myelin sheath. In addition, many of the tools developed in this project are useful for studying dynamic bifurcation phenomena, which occur in many other areas of science and engineering.

动力分岔现象的建模与分析 在科学和工程中很重要，因为实验 通常通过动态调整一个或多个参数来执行 直到不稳定导致过渡到一个新的观察状态 或行为。 使用数值和计算方法， 该项目将调查住宿现象， 空间不受限制的轴突和有髓鞘的神经节段。 一 主要目标是建立 无源负载（导电和电容）， 调节神经细胞以及它如何影响信号传导。 的 项目需要计算和分析分叉研究 具有缓变边界的反应扩散方程组， 界面条件 另一个目标是分类和 探索不同种类的随机波动如何影响 神经模型中的调节。 随机摄动法 退出时间估计和数值模拟将是 就业。 在神经科学中，阈值和调节实验， 细胞水平通过缓慢去极化 通过斜升或逐步增加施加的电流使膜兴奋。 这些实验研究调节现象， 空间上不受限制的轴突和有髓鞘的神经节段被 对于理解传导故障发生的原因和方式非常重要 在部分脱髓鞘的神经;衰弱性疾病， 多发性硬化可引起部分脱髓鞘病变 髓鞘 此外，许多开发的工具， 这对研究动力分岔问题是有益的 现象，发生在许多其他领域的科学和 工程.