勷勤数学•专家报告

题      目：昼夜节律调节阈值动力学对睡眠-觉醒转换机制建模

报  告  人： 姚成贵 教授  (邀请人：邹为)

                                       嘉兴大学

时      间： 11月9日  09：00-10:00

地     点：数科院东楼401

报告人简介:

        姚成贵，博士，嘉兴大学教授。入选浙江省高校领军人才培养计划高层次拔尖人才，浙江省高校中青年学科带头人。2011年于中科院武汉物理与数学研究所获得理学博士学位。主要研究方向：睡眠动力学，非线性动力学，神经动力学及其数学建模。目前发表SCI论文50余篇，主持完成国家自然科学基金面上项目，主持完成国家自然科学基金青年基金项目，浙江省自然科学基金面上项目，中国博士后基金。

摘      要：

       Human sleep-wake cycles emerge from complex interactions between homeostatic sleep pressure and circadian rhythms. In this study, we extend the Phillips-Robinson model by introducing circadian-dependent dynamic thresholds for sleep and wake transitions, yielding a more physiologically grounded framework for sleep regulation. Using bifurcation analysis, we show that the transition from sustained wakefulness to rhythmic sleep-wake cycles is governed by a saddle-node on invariant circle (SNIC) bifurcation, and that these oscillations become entrained to external 24 h light-dark cues. We analytically derive circadian  modulated sleep and wake thresholds, revealing how the interaction between circadian and homeostatic drives governs sleep-wake transitions. Our model captures key physiological phenomena, including: (1)the onset and entrainment of sleep-wake rhythms, (2) immediate sleep onset and partial rebound following sleep deprivation, and (3) sleep fragmentation under shift work-like conditions. These results offer new mechanistic insights into how circadian misalignment alters sleep timing and quality. Together, our findings establish an updated theoretical framework for modeling sleep-wake regulation in both natural and disrupted environments, with implications for shift work management, sleep disorder interventions, and personalized chronotherapy.

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