Analysis of circadian rhythm synchronization under the influence of pain

The synchronization of biological rhythms is of fundamental importance for health. The influence of pain on the functioning of vital functions and its effects on the synchronization of biological rhythms in human beings have been explored clinically for a long time. On the other hand, the modeling of this phenomenon can add features that are still unexplored. This bias fits the present contribution: to analyze the existence of synchronization of the circadian rhythm under the influence of external factors such as pain. To that end, we propose and investigate a model of coupled and phase oscillators that describes the sleep-wake, body temperature, and pain rhythms. The simplicity of the modeling allows one to obtain the synchronized solutions analytically as well as derive restrictions in terms of the parameters that guarantee their synchronization. The results obtained by analyzing the proposed model are accompanied by numerical simulations.