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

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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.