一种无输入$\mathcal{O}(ε)$约束的自适应相位幅度降低框架
An Adaptive Phase-Amplitude Reduction Framework Without $\mathcal{O}(ε)$ Constraints on Inputs
摘要：
相位缩减是一种成熟的技术，用于分析响应于弱外部输入的振荡的定时。在过去的几十年中，已经获得了各种各样的结果，弱扰动振荡器的输入或输入的时间导数的大小上的限制性限制。相比之下，没有一般的减少技术，目前存在的任意，大幅度的输入和相对很少了解这些强烈扰动的极限环振荡器的振荡动力学分析。在这项工作中，等稳约化理论被用来开发一种自适应相位-振幅变换，该变换对允许输入没有任何限制。此外，提供的一些Floquet乘数的基本周期轨道接近零，所提出的方法产生的减少的维度相比，其他相位振幅减少框架。数值计算表明，该方法准确地反映了同步和夹带的耦合振子的制度，各种其他相位振幅减少失败。
英文摘要：
Phase reduction is a well-established technique used to analyze the timing of oscillations in response to weak external inputs. In the preceding decades, a wide variety of results have been obtained for weakly perturbed oscillators that place restrictive limits on the magnitude of the inputs or on the magnitude of the time derivatives of the inputs. By contrast, no general reduction techniques currently exist to analyze oscillatory dynamics in response to arbitrary, large magnitude inputs and comparatively very little is understood about these strongly perturbed limit cycle oscillators. In this work, the theory of isostable reduction is leveraged to develop an adaptive phase-amplitude transformation that does not place any restrictions on the allowable input. Additionally, provided some of the Floquet multipliers of the underlying periodic orbits are near-zero, the proposed method yields a reduction in dimension comparable to that of other phase-amplitude reduction frameworks. Numerical illustrations show that the proposed method accurately reflects synchronization and entrainment of coupled oscillators in regimes where a variety of other phase-amplitude reductions fail.
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