振子系综集体节律的相位重置
Phase resetting of collective rhythm in ensembles of oscillators
摘要：
相位重置曲线表征了具有集体周期行为的系统对扰动的响应方式。我们考虑坂口仓本振子的全局耦合系综，并利用系综演化理论推导出解析的相位重置方程。我们表明，最终的相位重置值由两部分组成：直接由扰动引起的即时相位重置，以及由扰动系统松弛回到其动态平衡而引起的动态相位重置。最后的相位复位曲线的解析，半解析和数值近似构造。我们支持我们的研究结果与广泛的数值证据，涉及相同和不相同的振荡器。我们的理论的有效性进行了讨论的背景下，大合奏近似的热力学极限。
英文摘要：
Phase resetting curves characterize the way a system with a collective periodic behavior responds to perturbations. We consider globally coupled ensembles of Sakaguchi-Kuramoto oscillators, and use the Ott-Antonsen theory of ensemble evolution to derive the analytical phase resetting equations. We show the final phase reset value to be composed of two parts: an immediate phase reset directly caused by the perturbation, and the dynamical phase reset resulting from the relaxation of the perturbed system back to its dynamical equilibrium. Analytical, semi-analytical and numerical approximations of the final phase resetting curve are constructed. We support our findings with extensive numerical evidence involving identical and non-identical oscillators. The validity of our theory is discussed in the context of large ensembles approximating the thermodynamic limit.
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