A geometric theory for non-standard relaxation oscillators

非标准张弛振荡器的几何理论

• 批准号: DP180103022
• 负责人: Prof Martin Wechselberger
• 金额: $ 28.11万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2018
• 资助国家: 澳大利亚
• 起止时间: 2018-01-01 至 2021-10-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP180103022
• 关键词: geometric; theory; non; standard; relaxation

This project aims to develop new geometric methods for the analysis of multi-scale models of biological rhythms, and design diagnostic tools to identify key parameters that cause and control these signals. Rhythms, such as breathing, neural and cardiac rhythms and pulsatile hormone secretion, are central for life. Many important biochemical cell signals exhibiting relaxation-type behaviour cannot be rigorously analysed with standard dynamical systems tools due to an inherent non-uniform time-scale splitting in these models. This project aims to develop a unified mathematical theory that weaves together results from geometric singular perturbation theory and algebraic geometry to explain the genesis of complex rhythms and patterns in biological, non-standard, multi-scale systems, both at individual and network level.

该项目旨在开发新的几何方法来分析生物节律的多尺度模型，并设计诊断工具来识别引起和控制这些信号的关键参数。节奏，如呼吸，神经和心脏的节奏和脉动激素分泌，是生命的核心。 许多重要的生化细胞信号表现出松弛型行为不能严格分析与标准的动力系统工具，由于在这些模型中固有的非均匀的时间尺度分裂。该项目旨在开发一个统一的数学理论，将几何奇异摄动理论和代数几何的结果编织在一起，以解释生物，非标准，多尺度系统中复杂节奏和模式的起源，无论是在个人还是网络层面。