Multi-frequency oscillations in biological, electrical, and mechanical systems

生物、电气和机械系统中的多频振荡

• 批准号: 0708331
• 负责人: Yingfei Yi
• 金额: $ 40.97万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-06-15 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0708331&HistoricalAwards=false
• 关键词: Multi; frequency; oscillations; biological; electrical

Proposal: DMS-0708331Principal Investigator: Yi, YingfeiInstitution: GA TechProposal Title: Multi-frequency oscillations in biological, electrical, and mechanical systemsABSTRACTThe project focuses on a continuing study of multi-frequency phenomena arising in biological, electrical, and mechanical oscillatory systems with or without damping. It consists of three separate but closely related parts: 1. Quasi-periodic motions; 2. Almost automorphic intermittency; 3. Bio-chemical oscillations. Part 1 of the project concerns the study of quasi-periodic phenomena in three important classes of conservative systems: properly degenerate, nearly integrable Hamiltonian systems, Poisson-Hamilton systems, and Hamiltonian networks.Part 2 of the project is devoted to the study of two general dynamical intermittencies: Strange, non-chaotic attractors in damped, quasi-periodically forced, nonlinear oscillatory systems and Cantori in nearly integrable conservative systems. Part 3 of the project contains a program of developing generic bio-chemical models and studying the underlying fluctuating bio-chemical oscillations.The project focuses on a continuing study of 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 much complex dynamical outcomes oscillating in multi-phases. But the mechanism of such complexity is far from being well-understood. The main goal of the proposed project is to develop a mathematical theory toward making a fundamental understanding of such complexity.

项目编号：dms -0708331项目负责人：易颖飞机构名称：GA TechProposal题目：生物、电气和机械系统中的多频振荡摘要本项目主要研究生物、电气和机械振荡系统中存在或不存在阻尼的多频现象。它由三个独立但密切相关的部分组成：准周期性的运动;2. 几乎自同构间歇性；3. 生化振荡。本课题的第一部分研究了三种重要的保守系统中的拟周期现象：适当简并、近可积哈密顿系统、泊松-哈密顿系统和哈密顿网络。该项目的第二部分致力于研究两种一般的动力间歇性：阻尼，准周期强迫，非线性振荡系统中的奇异，非混沌吸引子和近可积保守系统中的Cantori。该项目的第三部分包含一个开发通用生化模型和研究潜在的波动生化振荡的程序。该项目侧重于对自然界中多频现象的持续研究，特别是那些在生物、电气和机械系统中出现的现象。大量的实验和计算机模拟表明，涉及多频的物理系统可以产生非常复杂的多相振荡动力学结果。但这种复杂性的机制还远未被充分理解。该计划的主要目标是发展一种数学理论，从而对这种复杂性有一个基本的理解。