Multi-Frequency Oscillations and Applications in Communications Systems

多频振荡及其在通信系统中的应用

• 批准号: 9803581
• 负责人: Yingfei Yi
• 金额: $ 8.39万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9803581&HistoricalAwards=false
• 关键词: Multi; Frequency; Oscillations; Applications; Communications

This project concerns the study of multi-frequency oscillations arising in almost periodically forced oscillators and self-excited systems. Main problems to be considered are the nature of complicated dynamics resulting from the interactions of several frequencies especially when these frequencies are close to resonance. By studying issues such as mean motions of toral flows and quasi-periodic bifurcations, the investigator would like to address the important role played by almost automorphic oscillations in these systems. The results of this project will have significant applications to electric circuit designs of crystal oscillators.This project is devoted to the study of mathematical models of physical systems that present multi-phase oscillations (e.g., mechanical devices and electric circuits) or systems that are subjected to seasonal variations (e.g., biological oscillators and population models). Due to the complexity of these physical systems involving large dimension, multi-parameters and many oscillating frequencies, qualitative analysis (with help of numerical computations) will be extremely important to guide practical designs of the physical systems with respect to the prediction of valuable design parameters and the explanation of new oscillatory phenomena etc. In particular, the results of this project will be of a great impact on electric circuit designs of crystal oscillators arising in a large variety of applications of communication systems.

本课题主要研究准周期受迫振子和自激系统中的多频振荡。要考虑的主要问题是由几个频率的相互作用引起的复杂动力学的性质，特别是当这些频率接近共振时。通过研究对流的平均运动和准周期分叉等问题，研究者希望解决几乎自同构的振荡在这些系统中所起的重要作用。本项目致力于研究存在多相振荡的物理系统(如机械设备和电路)或受季节变化影响的系统(如生物振荡器和种群模型)的数学模型。由于这些物理系统的复杂性，涉及大尺寸、多参数、多振荡频率，定性分析(借助数值计算)对于指导物理系统的实际设计，对于预测有价值的设计参数和解释新的振荡现象等将是非常重要的，特别是本项目的结果将对通信系统中的各种应用中出现的晶体振荡器的电路设计产生重大影响。