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

提案：DMS-0708331主要研究员：易英飞机构：GA技术提案标题：生物，电气和机械系统中的多频振荡摘要该项目的重点是持续研究生物，电气和机械振荡系统中出现的多频现象，有或没有阻尼。它由三个独立但密切相关的部分组成：1。准周期运动; 2.几乎自同构的不对称性; 3.生化振荡。 该项目的第一部分涉及三个重要的保守系统类的准周期现象的研究：适当退化，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两个一般的动力学方程的研究：阻尼，准周期强迫，非线性振动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括开发通用生化模型和研究潜在的波动生化振荡的计划。该项目侧重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进行持续研究。大量的实验和计算机模拟表明，多频物理系统可以产生多相振荡的复杂动力学结果。但是，这种复杂性的机制还远未得到很好的理解。该项目的主要目标是开发一种数学理论，以便对这种复杂性进行基本理解。

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.