强调幅高频力扰动下极限环振子的相位缩减
Phase reduction of a limit cycle oscillator perturbed by a strong amplitude-modulated high-frequency force
摘要：
研究了强调幅高频力作用下极限环振子的相位缩减方法。通过引入一种新的有效相位响应曲线，导出了相位动力学方程。我们表明，如果有效的相位响应曲线是到处都是正（负），那么夹带的振荡器的包络频率是可能的，只有当这个频率是高于（低于）的振荡器的固有频率。此外，通过使用庞特里亚金最大值原理，我们推导出了一个最佳波形的扰动，确保夹带的振荡器具有最小的功率。用Stuart-Landau振子和模型神经元证明了理论结果。
英文摘要：
The phase reduction method for a limit cycle oscillator subjected to a strong amplitude-modulated high-frequency force is developed. An equation for the phase dynamics is derived by introducing a new, effective phase response curve. We show that if the effective phase response curve is everywhere positive (negative), then an entrainment of the oscillator to an envelope frequency is possible only when this frequency is higher (lower) than the natural frequency of the oscillator. Also, by using the Pontryagin maximum principle, we have derived an optimal waveform of the perturbation that ensures an entrainment of the oscillator with minimal power. The theoretical results are demonstrated with the Stuart-Landau oscillator and model neurons.
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