Multi-frequency Oscillations: Regularity, Irregularity, and Complexity

点击翻译按钮获取中文摘要

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.