Circadian rhythm synchronization under the influence of pain: PIM model with memory

In this work, we propose and analyze the existence of synchronization/dissynchronization states of in-phase and coupled oscillators that model the influence of external factors such as pain on the biological rhythms of sleep-wakefulness and body temperature under the memory effect. We show the well-posedness of the proposed model and derive analytical solutions for the oscillator system in the synchronized state. The theoretical results are accompanied by some numerical simulations that indicate that the existence of memory contributes to the synchronization of the oscillator system.