A BEGINNERS GUIDE TO LIMIT-CYCLES, THEIR USES AND ABUSES
A BEGINNERS GUIDE TO LIMIT-CYCLES, THEIR USES AND ABUSES
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DOI：
10.1080/09291019509360337
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发表时间：
1995-05-01
影响因子：
1.1
通讯作者：
LAKINTHOMAS, PL
中科院分区：
文献类型：
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作者：
LAKINTHOMAS, PL
振荡器的数学模型分为两大类，简单（一维）和非简单（二维或多维）。用于描述节律系统的模型类型会影响实验设计和解释，简单和非简单模型会做出非常不同的实验预测。非简单振子的基本性质与简单振子不同，它们是0型重置、相位奇异性和振幅变化。非简单振荡器的两个例子是可调振幅振荡器（如无摩擦摆）和吸引极限环。振荡器的群体可能表现出广泛的动态行为，包括可调振幅或极限环，这取决于单个振荡器的性质和它们之间的耦合。简单的振荡器模型可能适用于某些生物系统，如发育周期和细胞周期，而昼夜节律振荡器最好由能够同时进行幅度变化和稳定夹带的群体来建模。
Mathematical models of oscillators fall into two major categories, simple (one-dimensional) and non-simple (two-or-more dimensional). The type of model used to describe a rhythmic system will influence experimental design and interpretation, and very different experimental predictions are made by simple and non-simple models. The basic properties of non-simple oscillators that are not shared with simple oscillators are Type 0 resetting, phase singularities, and amplitude changes. Two examples of non-simple oscillators are adjustable-amplitude oscillators (such as the frictionless pendulum) and attracting limit cycles. Populations of oscillators may exhibit a wide range of dynamic behaviour, including an adjustable amplitude or a limit cycle, depending on the nature of the individual oscillators and the coupling between them. Simple oscillator models may be appropriate to some biological systems such as developmental cycles and cell cycles, while circadian oscillators are best modelled by populations capable of both amplitude changes and stable entrainment.