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

建议：DMS-0708331主要研究员：易，英飞研究所：GA技术建议标题：生物、电气和机械系统中的多频振荡摘要本项目致力于对生物、电气和机械振动系统中出现的多频现象进行持续的研究。它由三个独立但密切相关的部分组成：1.准周期运动；2.几乎自同构间歇性；3.生化振荡。第一部分研究了三类重要保守系统中的准周期现象：适当退化的近可积哈密顿系统、泊松-哈密顿系统和哈密顿网络。第二部分研究了两类一般的动力学间歇性：有阻尼、准周期强迫的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坎托里吸引子。该项目的第三部分包括开发通用生物化学模型和研究潜在的波动生物化学振荡的计划。该项目专注于对自然界中的多频率现象，特别是生物、电气和机械系统中出现的多频率现象的持续研究。许多实验和计算机模拟预测，涉及多个频率的物理系统可以产生复杂的多相振荡的动力学结果。但这种复杂性的机制还远未得到很好的理解。拟议项目的主要目标是发展一种数学理论，以期从根本上理解这种复杂性。

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.