Global computation of phase-amplitude reduction for limit-cycle dynamics.
Global computation of phase-amplitude reduction for limit-cycle dynamics.
复制标题
极限环动力学的相位幅度缩减的全局计算。
作者：
A. Mauroy;I. Mezić
近年来，人们对极限环动力学的相位降幅问题越来越感兴趣。在相位坐标上增加一个振幅坐标使我们能够考虑到极限环的横向动力学，从而克服了经典相位缩减的主要局限性（极限环的强收敛性和弱输入）。以往的研究大多集中于局部量，如无穷小响应，而相位-幅度缩减的一个主要和限制性挑战是在极限环的吸引力盆地中计算全局幅度坐标。在本文中，我们提出了一种计算大坐标系中完整相幅坐标的方法。我们的方法基于所谓的Koopman（复合）算子，旨在通过拉普拉斯平均（结合谐波平衡法）计算算子的特征函数。这就产生了一种不局限于二维系统的前向积分方法。我们通过计算所谓的二维、三维和四维状态空间中的极限环等稳态，以及它们对强外部输入的响应来说明该方法。
Recent years have witnessed increasing interest in phase-amplitude reduction of limit-cycle dynamics. Adding an amplitude coordinate to the phase coordinate allows us to take into account the dynamics transversal to the limit cycle and thereby overcome the main limitations of classic phase reduction (strong convergence to the limit cycle and weak inputs). While previous studies, mostly focus on local quantities such as infinitesimal responses, a major and limiting challenge of phase-amplitude reduction is to compute amplitude coordinates globally, in the basin of attraction of the limit cycle. In this paper, we propose a method to compute the full set of phase-amplitude coordinates in the large. Our method is based on the so-called Koopman (composition) operator and aims at computing the eigenfunctions of the operator through Laplace averages (in combination with the harmonic balance method). This yields a forward integration method that is not limited to two-dimensional systems. We illustrate the method by computing the so-called isostables of limit cycles in two-, three-, and four-dimensional state spaces, as well as their responses to strong external inputs.
具有强强迫或耦合的振荡器的相位响应函数
DOI：
10.1209/0295-5075/118/50006
发表时间：
2017
期刊：
Europhysics Letters
影响因子：
--
作者：
V. Klinshov;S. Yanchuk;A. Stephan;V. Nekorkin
通讯作者：
V. Nekorkin
影响因子：
3.4
作者：
Oprisan, SA;Prinz, AA;Canavier, CC
通讯作者：
Canavier, CC