Tyloo M, Delabays R, Jacquod Ph
Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
School of Engineering, University of Applied Sciences of Western Switzerland HES-SO, CH-1951 Sion, Switzerland.
Phys Rev E. 2019 Jun;99(6-1):062213. doi: 10.1103/PhysRevE.99.062213.
Complex physical systems are unavoidably subjected to external environments not accounted for in the set of differential equations that models them. The resulting perturbations are standardly represented by noise terms. If these terms are large enough, they can push the system from an initial stable equilibrium point, over a nearby saddle point, outside of the basin of attraction of the stable point. Except in some specific cases, the distance between these two points is not known analytically. Focusing on Kuramoto-like models and under simple assumptions on this distance, we derive conditions under which such noise terms perturb the dynamics strongly enough that they lead to stochastic escape from the initial basin of attraction. We numerically confirm the validity of that criterion for coupled oscillators on four very different complex networks. We find in particular that, quite counterintuitively, systems with inertia leave their initial basin faster than or at the same time as systems without inertia, except for strong white-noise perturbations.
复杂物理系统不可避免地会受到外部环境的影响，而这些外部环境在对其进行建模的微分方程组中并未得到考虑。由此产生的扰动通常由噪声项来表示。如果这些项足够大，它们可以将系统从初始稳定平衡点推离，经过附近的鞍点，使其超出稳定点吸引域的范围。除了某些特定情况外，这两点之间的距离无法通过解析方法得知。我们聚焦于类Kuramoto模型，并在对该距离的简单假设下，推导出了这样的噪声项对动力学产生足够强烈的扰动从而导致从初始吸引域随机逃逸的条件。我们通过数值方法证实了该准则对于四个非常不同的复杂网络上的耦合振子的有效性。我们特别发现，相当违反直觉的是，除了强白噪声扰动外，有惯性的系统比没有惯性的系统更快或同时离开其初始吸引域。
