Isostable reduction of oscillators with piecewise smooth dynamics and complex Floquet multipliers.
Isostable reduction of oscillators with piecewise smooth dynamics and complex Floquet multipliers.
复制标题
具有分段平滑动力学和复杂 Floquet 乘法器的振荡器的等稳态还原。
DOI：
10.1103/physreve.99.022210
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Dan Wilson
中科院分区：
文献类型：
--
作者：
Dan Wilson
相幅减缩是极限环振子研究中的一种广泛应用的技术，它能够在更容易解析的坐标集中表示复杂的高维动力系统。最近的工作主要集中在等稳坐标的使用上，该坐标表征了溶液向周期轨道的瞬时衰减，并最终可用于提高这些简化模型的精度。然而，这种相位幅度减小策略可以应用到的系统的范围仍然相当有限。在这项工作中，进一步发展了使用等稳坐标的相位-幅度减少理论，以适应更广泛的动力系统集。在第一部分中，我们考虑了分段光滑动力系统的极限环，并发展了相应的策略来计算相关的约化方程。在第二部分中，引入了复值Floquet乘子等稳坐标的概念，使得每一对复共轭Floquet乘子都有一个类相位坐标和一个类振幅坐标。给出了与可兴奋心肌细胞的分段光滑表示相关的例子，并讨论了简化坐标系与心脏交替出现之间的关系。同时，对具有复数Floquet乘子的混沌外力摆系统进行了相位幅度减小，并研究了其周期解镇定的控制策略。
Phase-amplitude reduction is a widely applied technique in the study of limit cycle oscillators with the ability to represent a complicated and high-dimensional dynamical system in a more analytically tractable set of coordinates. Recent work has focused on the use of isostable coordinates, which characterize the transient decay of solutions toward a periodic orbit, and can ultimately be used to increase the accuracy of these reduced models. The breadth of systems to which this phase-amplitude reduction strategy can be applied, however, is still rather limited. In this work, the theory of phase-amplitude reduction using isostable coordinates is further developed to accommodate a broader set of dynamical systems. In the first part, limit cycles of piecewise smooth dynamical systems are considered and strategies are developed to compute the associated reduced equations. In the second part, the notion of isostable coordinates for complex-valued Floquet multipliers is introduced, resulting in one phaselike coordinate and one amplitudelike coordinate for each pair of complex conjugate Floquet multipliers. Examples are given with relevance to piecewise smooth representations of excitable cardiomyocytes and the relationship between the reduced coordinate system and the emergence of cardiac alternans is discussed. Also, phase-amplitude reduction is implemented for a chaotic, externally forced pendulum with complex Floquet multipliers and a resulting control strategy for the stabilization of its periodic solution is investigated.
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影响因子：
2.4
作者：
Boland, Richard P.;Galla, Tobias;McKane, Alan J.
通讯作者：
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使用等稳态坐标进行相位还原的更高精确度和更广泛的适用性
影响因子：
1.9
作者：
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通讯作者：
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影响因子：
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作者：
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通讯作者：
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影响因子：
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作者：
Iyer, V;Mazhari, R;Winslow, RL
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DOI：
10.1152/ajpheart.00747.2003
发表时间：
2004-06-01
影响因子：
4.8
作者：
Cherry, EM;Fenton, FH
通讯作者：
Fenton, FH