Multi-Frequency Oscillations and Applications in Communications Systems

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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.