论文标题
无需$ \ mathcal {o}（ε）$约束的自适应相位振幅降低框架
An Adaptive Phase-Amplitude Reduction Framework Without $\mathcal{O}(ε)$ Constraints on Inputs
论文作者
论文摘要
相减少是一种良好的技术，用于分析响应弱外部输入的振荡时间。在过去的几十年中，对于弱扰动的振荡器，已经获得了各种各样的结果，这些振荡器将限制限制放在输入的大小或输入的时间导数的大小上。相比之下，目前尚无一般还原技术来分析响应于任意，大量输入的振荡动力学，并且关于这些强烈扰动的极限循环振荡器的理解很少。在这项工作中，利用同等减少的理论来开发自适应相位振幅转换，该转换不会对允许输入施加任何限制。此外，只要基础周期轨道的某些浮子乘数接近零，则该方法的尺寸与其他相位振幅降低框架相当。数值插图表明，所提出的方法准确地反映了在各种其他相位振幅降低失败的方案中耦合振荡器的同步和夹带。
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.
