Statistical models of coupled dynamical systems and the transition from weak to strong coupling

The statistical model for steady‐state response of a coupled dynamical system that is used in both room acoustics and statistical energy analysis is taken as the hypothesis. The model is defined by the fundamental equations of linear relation between the response energies of the subsystems and the input powers. Additional restrictions arise from the principle of reciprocity. The model is used to examine the effect of variable strength of coupling between the subsystems and the transition from weak to strong coupling. Results familiar from modal analysis [J. Acoust. Soc. Am. 63, 1081–1083 (1978)] are derived without introducing modal concepts.