Global and local responses of coupled dynamic systems

Abstract

Responses of a master oscillator coupled to a set of satellite oscillators are evaluated. A set is designed by specifying a normalized frequency distribution. When the designed distribution is completely degenerate, the influence of the coupling is global. The coupling generates two global peaks, one on each side of an antiresonance that replaces the peak in the response of the uncoupled master oscillator. The loss factor for these global peaks matches that of the uncoupled master oscillator. As the degeneracy is gradually removed, the evaluated response gradually reveals, within the distribution bandwidth, contributions from individual satellite oscillators. The loss factors and the frequency separation of the two global peaks then become dependent upon the coupling. As the degeneracy is further removed, the local presence of the satellite oscillators assumes the dominant feature in the response whereas the presence of the two global peaks subsides. Since the designed distributions relate loss factors directly to modal overlap parameters, increases in these parameters above unity render this dominance in the response quiescent and saturated. On the other hand, continuous decreases in these parameters below unity increase the fluctuations in that dominant part of the response ad infinitum.