勷勤数学•专家报告

题      目：The dynamical mechanism for the ultradian rhythm

报  告  人：姚成贵  教授  (邀请人：邹为)

                                    嘉兴大学

时      间：11月30日  10：00-11：00

地     点：数科院西楼111报告厅

报告人简介:

       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：

       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 successfuly 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.

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