An Operational Definition of Phase Characterizes the Transient Response of Perturbed Limit Cycle Oscillators
An Operational Definition of Phase Characterizes the Transient Response of Perturbed Limit Cycle Oscillators
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DOI：
10.1137/17m1153261
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发表时间：
2018-10
期刊：
影响因子：
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通讯作者：
Dan Wilson;B. Ermentrout
中科院分区：
文献类型：
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作者：
Dan Wilson;B. Ermentrout
相位约化是研究受扰极限环振子的重要工具。通常，相位是相对于一些渐近极限来定义的，这常常使得相位归约在接近极限环期间预测瞬态行为的能力不足。在这项工作中，我们提出了一个可操作的概念的相位，定义相对于一个独特的功能的振荡器，例如，定时定期发射神经元的动作电位。我们推导出标准和操作阶段减少之间的关系，以使这两种方法之间的比较。在理论和数值算例中，我们展示了如何准确地预测由于扰动的渐近和瞬态行为，而不依赖于高阶相位响应曲线的概念，这是有效的，只为特定的扰动。此外，我们开发了一个战略，直接测量的必要条件的操作阶段减少时，充分的动态…
Phase reduction is an essential tool used in the study of perturbed limit cycle oscillators. Usually, phase is defined with respect to some asymptotic limit, often making phase reduction's ability to predict transient behavior during the approach to a limit cycle inadequate. In this work, we present an operational notion of phase, defined with respect to a distinct feature of the oscillator, for example, the timing of a periodically firing neuron's action potential. We derive relationships between standard and operational phase reduction in order to make comparisons between these two approaches. In theoretical and numerical examples, we show how operational phase reduction accurately predicts both the asymptotic and transient behavior due to perturbations without relying on the notion of higher order phase response curves which are valid only for specific perturbations. Furthermore, we develop a strategy for direct measurement of the necessary terms of the operational phase reduction when the full dynamic...