Wilson Dan
Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, Tennessee 37996, USA.
Phys Rev E. 2020 Feb;101(2-1):022220. doi: 10.1103/PhysRevE.101.022220.
While phase reduction is a well-established technique for the analysis of perturbed limit cycle oscillators, practical application requires perturbations to be sufficiently weak thereby limiting its utility in many situations. Here, a general strategy is developed for constructing a set of phase-amplitude reduced equations that is valid to arbitrary orders of accuracy in the amplitude coordinates. This reduction framework can be used to investigate the behavior of oscillatory dynamical systems far beyond the weakly perturbed paradigm. Additionally, a patchwork phase-amplitude reduction method is suggested that is useful when exceedingly large magnitude perturbations are considered. This patchwork method incorporates the high-accuracy phase-amplitude reductions of multiple nearby periodic orbits that result from modifications to nominal parameters. The proposed method of high-accuracy phase-amplitude reduction can be readily implemented numerically and examples are provided where reductions are computed up to fourteenth order accuracy.
虽然相位约化是分析受扰极限环振荡器的一种成熟技术，但实际应用要求扰动足够弱，从而限制了其在许多情况下的实用性。在此，我们开发了一种通用策略，用于构建一组相位 - 振幅约化方程，该方程在振幅坐标中具有任意精度阶次的有效性。这种约化框架可用于研究远远超出弱扰动范式的振荡动力系统的行为。此外，还提出了一种拼凑相位 - 振幅约化方法，当考虑极大幅度的扰动时该方法很有用。这种拼凑方法结合了由标称参数修改产生的多个附近周期轨道的高精度相位 - 振幅约化。所提出的高精度相位 - 振幅约化方法可以很容易地在数值上实现，并提供了计算精度高达十四阶约化的示例。
