Multi-frequency Oscillations: Regularity, Irregularity, and Complexity

多频振荡：规则性、不规则性和复杂性

• 批准号: 1109201
• 负责人: Yingfei Yi
• 金额: $ 28.5万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1109201&HistoricalAwards=false
• 关键词: Multi; frequency; Oscillations; Regularity; Irregularity

The project focuses on multi-frequency phenomena arising in biological, electrical and mechanical oscillatory systems with or without damping. It consists of two separate but closely related parts: 1. Quasi-periodic and weakly quasi-periodic motions; 2. Biological oscillations and complexities. Part 1 of the project aims at the study of the existence, stability, and mechanism for both regular and irregular multifrequency oscillations in properly degenerate Hamiltonian systems, Poisson-Hamilton systems, and Hamiltonian networks. Part 2 of the project is devoted to the study of biological oscillations and complexity in bio-chemical reaction systems and bio-networks, in both deterministic and stochastic settings, with respect to issues such as stransient oscillations, stochastic oscillations, stability of invariant measures, and the connections among degeneracy, robustness, and system complexity.The project focuses on multi-frequency phenomena in nature especially those arising in biological, electrical, and mechanical systems. It is predicted by many experiments and computer simulations that physical systems involving multi-frequency can produce many complex dynamical outcomes oscillating in multiple phases. But the mechanism of such complexity is far from well-understood, especially when ambient noise is present. In the project, the PI plans to develop a mathematical theory towards a fundamental understanding of such complexity.

该项目侧重于有或没有阻尼的生物、电气和机械振荡系统中出现的多频现象。它由两个独立但密切相关的部分组成：准周期运动和弱准周期运动；2. 生物振荡和复杂性。本课题的第一部分旨在研究适当简并哈密顿系统、泊松-哈密顿系统和哈密顿网络中规则和不规则多频振荡的存在性、稳定性和机制。该项目的第二部分致力于研究生物化学反应系统和生物网络中的生物振荡和复杂性，在确定性和随机设置下，涉及诸如瞬态振荡，随机振荡，不变测度的稳定性以及退化，鲁棒性和系统复杂性之间的联系等问题。该项目侧重于自然界中的多频现象，特别是那些在生物、电气和机械系统中产生的现象。许多实验和计算机模拟预测，涉及多频的物理系统可以产生许多复杂的多相振荡动力学结果。但是这种复杂性的机制还远没有被很好地理解，特别是当环境噪声存在的时候。在这个项目中，PI计划开发一种数学理论，以从根本上理解这种复杂性。