The mammalian circadian clock is well-known to be important for our sleep–wake cycles, as well as other daily rhythms such as temperature regulation, hormone release or feeding–fasting cycles. Under normal conditions, these daily cyclic events follow 24 h limit cycle oscillations, but under some circumstances, more complex nonlinear phenomena, such as the emergence of chaos, or the splitting of physiological dynamics into oscillations with two different periods, can be observed. These nonlinear events have been described at the organismic and tissue level, but whether they occur at the cellular level is still unknown. Our results show that period-doubling, chaos and splitting appear in different models of the mammalian circadian clock with interlocked feedback loops and in the absence of external forcing. We find that changes in the degradation of clock genes and proteins greatly alter the dynamics of the system and can induce complex nonlinear events. Our findings highlight the role of degradation rates in determining the oscillatory behaviour of clock components, and can contribute to the understanding of molecular mechanisms of circadian dysregulation.

中文翻译：

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生物钟模型中的非线性现象


众所周知，哺乳动物的生物钟对于我们的睡眠-觉醒周期以及其他日常节律（例如温度调节、激素释放或进食-禁食周期）非常重要。在正常情况下，这些每日循环事件遵循24小时极限循环振荡，但在某些情况下，可以观察到更复杂的非线性现象，例如混沌的出现，或生理动力学分裂为两个不同周期的振荡。这些非线性事件已经在有机体和组织水平上进行了描述，但它们是否发生在细胞水平上仍然未知。我们的结果表明，在没有外力的情况下，具有互锁反馈环路的哺乳动物生物钟的不同模型中会出现周期倍增、混沌和分裂。我们发现时钟基因和蛋白质降解的变化极大地改变了系统的动力学，并可能引发复杂的非线性事件。我们的研究结果强调了降解率在确定时钟组件振荡行为中的作用，并有助于理解昼夜节律失调的分子机制。