Relaxation Oscillations in a Class of Delay Differential Equations
Relaxation Oscillations in a Class of Delay Differential Equations
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一类时滞微分方程中的弛豫振荡
DOI：
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发表时间：
2002
影响因子：
1.9
通讯作者：
M. Mackey
中科院分区：
文献类型：
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作者：
A. Fowler;M. Mackey
本文研究了一类用于血液干细胞调控和动力学模型的时滞微分方程。在某些情况下，该模型表现出自我维持的振荡，周期可以显着长于基本的细胞周期时间。我们表明，在振荡的长周期发生时，细胞生成率是小的，我们提供了一个渐近分析的模型在这种情况下。这种分析与弛豫振荡器（如货车德尔波尔振荡器）的分析非常相似，只是在我们的情况下，慢流形是无限维的。尽管如此，对这个问题进行相当全面的分析是可能的。
We study a class of delay differential equations which have been used to model hematological stem cell regulation and dynamics. Under certain circumstances the model exhibits self-sustained oscillations, with periods which can be significantly longer than the basic cell cycle time. We show that the long periods in the oscillations occur when the cell generation rate is small, and we provide an asymptotic analysis of the model in this case. This analysis bears a close resemblance to the analysis of relaxation oscillators (such as the Van der Pol oscillator), except that in our case the slow manifold is infinite dimensional. Despite this, a fairly complete analysis of the problem is possible.