The 90-minute ultradian rhythm is a defining characteristic of human sleep, yet the underlying mechanism for this rhythm remains elusive. Here, we introduce a biologically plausible sleep model aimed at elucidating the intricate dynamical mechanisms that govern this phenomenon. Our model encapsulates both circadian and ultradian rhythms, shaping the architecture of sleep. It incorporates transitions between wakefulness, rapid eye movement (REM) sleep, and non-rapid eye movement (NREM) sleep, represented by "flip-flop" switches. By calibrating our model with empirically derived parameters, we have successfully replicated typical sleep patterns, accurately reproducing the 24-hour circadian rhythm alongside the 90-minute ultradian rhythm. Utilizing the theory of potential landscapes, we reveal the fundamental physical mechanisms that orchestrate transitions between different brain states. This provides a quantitative assessment of global stability, influenced by factors such as circadian drive, sleep homeostatic drive, and REM sleep pressure. To specifically investigate the ultradian rhythm, we streamline our comprehensive sleep model into a two-component framework focusing on NREM and REM sleep. This analytical reduction simplifies the potential function to a quartic two-well potential, clearly delineating NREM and REM sleep stages. By combining bifurcation analysis with the resonance principle, we propose that the 90-minute ultradian rhythm arises from the resonance between the weak ultradian drive and the simplified system.

Yao Chenggui, Ph.D., is a Professor at Jiaxing University. He has been selected into the High-Level Top-Tier Talents Program of the Zhejiang Provincial University Leading Talents Training Plan and recognized as a Young and Middle-Aged Academic Leader in Zhejiang Provincial Universities. He obtained his Doctor of Science degree from the Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences in 2011. His main research interests include sleep dynamics, nonlinear dynamics, neural dynamics, and their mathematical modeling. He has published over 50 SCI papers and presided over the completion of projects such as the General Program of the National Natural Science Foundation of China, the Young Scientists Fund Program of the National Natural Science Foundation of China, the General Program of the Zhejiang Provincial Natural Science Foundation, and the China Postdoctoral Science Foundation.