Multi-timescale systems and fast-slow analysis
Multi-timescale systems and fast-slow analysis
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DOI：
10.1016/j.mbs.2016.07.003
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发表时间：
2017-05-01
影响因子：
4.3
通讯作者：
Rubin, Jonathan E.
中科院分区：
文献类型：
--
作者：
Bertram, Richard;Rubin, Jonathan E.
生物系统的数学模型通常具有在不同时间尺度上变化的组件。这种多时间尺度的特性在进行计算机模拟时可能会导致问题，这可能需要大量的计算机时间，以便可以解决在最快时间尺度上变化的组件。这些多时间尺度系统的数学分析可以通过将它们划分为在不同时间尺度上演化的子系统来大大简化。然后，使用称为快-慢分析的技术半独立地分析子系统。在这篇综述中，我们描述了快-慢分析技术，并将其应用于弛豫振荡，神经元爆发振荡，鸭式振荡，混合模式振荡。虽然这些例子都涉及神经系统，但该技术可以并且已经应用于其他生物，化学和物理系统。这是一种强大的分析方法，随着新的实验技术推动生物模型的复杂性，它在未来将变得更加有用。(C)2016 Elsevier Inc. All rights reserved.
Mathematical models of biological systems often have components that vary on different timescales. This multi-timescale character can lead to problems when doing computer simulations, which can require a great deal of computer time so that the components that change on the fastest time scale can be resolved. Mathematical analysis of these multi-timescale systems can be greatly simplified by partitioning them into subsystems that evolve on different time scales. The subsystems are then analyzed semi-independently, using a technique called fast-slow analysis. In this review we describe the fast-slow analysis technique and apply it to relaxation oscillations, neuronal bursting oscillations, canard oscillations, and mixed-mode oscillations. Although these examples all involve neural systems, the technique can and has been applied to other biological, chemical, and physical systems. It is a powerful analysis method that will become even more useful in the future as new experimental techniques push forward the complexity of biological models. (C) 2016 Elsevier Inc. All rights reserved.