标题： 由非对称柯西噪声引起的集体振荡频率的非线性偏倚 显示英文标题

标题： Nonlinear bias of collective oscillation frequency induced by asymmetric Cauchy noise

摘要： 我们报告了受个体非对称柯西噪声驱动的正弦耦合相振子集体振荡频率的非线性偏置效应。噪声的不对称性使得 Ott-Antonsen 近似失效。我们论证了对于所有稳定的非高斯噪声，尾部不对称不仅是可能的（除了分布中位数的平凡平移外），而且在许多物理和生物物理设定中也是普遍存在的。为了理论描述这种效应，我们基于圆累积量发展了一种数学形式主义。在这个基础上可以推导出严格的渐近结果，但在传统的圆矩（Kuramoto-Daido 顺序参数）术语中似乎不可行。还详细报告了单个振子频率被全局振荡捕获的现象。基于低维圆累积量约化得到的理论结果的准确性通过用连分数方法计算的高精度“精确”解进行了验证。 显示英文摘要

摘要： We report the effect of nonlinear bias of the frequency of collective oscillations of sin-coupled phase oscillators subject to individual asymmetric Cauchy noises. The noise asymmetry makes the Ott-Antonsen Ansatz inapplicable. We argue that, for all stable non-Gaussian noises, the tail asymmetry is not only possible (in addition to the trivial shift of the distribution median) but also generic in many physical and biophysical set-ups. For the theoretical description of the effect, we develop a mathematical formalism based on the circular cumulants. The derivation of rigorous asymptotic results can be performed on this basis but seems infeasible in traditional terms of the circular moments (the Kuramoto-Daido order parameters). The effect of the entrainment of individual oscillator frequencies by the global oscillations is also reported in detail. The accuracy of theoretical results based on the low dimensional circular cumulant reductions is validated with the high-accuracy "exact" solutions calculated with the continued fraction method.