Graduate School of Information Science and Engineering, Tokyo Institute of Technology, O-okayama 2-12-1, Meguro, Tokyo 152-8552, Japan.
Phys Rev Lett. 2013 Nov 22;111(21):214101. doi: 10.1103/PhysRevLett.111.214101.
The phase reduction method for limit cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also applicable to strongly perturbed limit cycle oscillators. The fundamental assumption of our method is that the perturbations can be decomposed into a slowly varying component as compared to the amplitude relaxation time and remaining weak fluctuations. Under this assumption, we introduce a generalized phase parameterized by the slowly varying component and derive a closed equation for the generalized phase describing the oscillator dynamics. The proposed method enables us to explore a broader class of rhythmic phenomena, in which the shape and frequency of the oscillation may vary largely because of the perturbations. We illustrate our method by analyzing the synchronization dynamics of limit cycle oscillators driven by strong periodic signals. It is shown that the proposed method accurately predicts the synchronization properties of the oscillators, while the conventional method does not.
针对受弱扰的极限环振荡器的相减缩方法极大地促进了节律现象的理论研究。我们在此提出一种广义的相减缩方法，该方法也适用于强扰极限环振荡器。我们方法的基本假设是，与振幅弛豫时间相比，扰动可以分解为缓慢变化的分量，并且仍然是弱波动。在这个假设下，我们引入一个由缓慢变化分量参数化的广义相位，并为描述振荡器动力学的广义相位导出一个封闭方程。所提出的方法使我们能够探索更广泛的节律现象类别，其中由于扰动，振荡的形状和频率可能会有很大的变化。我们通过分析受强周期信号驱动的极限环振荡器的同步动力学来说明我们的方法。结果表明，所提出的方法可以准确地预测振荡器的同步特性，而传统方法则不能。
