Improved reduced order model for study of coupled phenomena

Many interesting phenomena in applications are based on interactions between their constituent sub-systems. The first principle exact models of these phenomena can be quite complicated. Therefore, many practitioners prefer to use so-called phenomenological models, which are generally known as models based on coupled mode theory (CMT). This type of reduced-order model captures the dominant behavior of the system under appropriate conditions. Quite often, these validity conditions are qualitatively described, but no detailed mathematical analysis is provided. This work addresses this issue and presents improvements in the traditional phenomenological models. Although an LC circuit model is used for illustration due to its simplicity, the results in this work are equally applicable to a wide variety of coupled models. A detailed mathematical analysis is carried out to quantify the order of approximation involved in the model-based CMT. Using it, the validity of the model in the regime from weak coupling to strong coupling is analytically investigated. An improved reduced-order model is proposed, which gives better results than the traditional phenomenological model. The analytical studies are verified with numerical simulations, which clearly show better validity of the proposed improved model of coupled systems.