Acebrón J A, Rappel W-J, Bulsara A R
Department of Physics, University of California, San Diego, La Jolla, California 92093, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jan;67(1 Pt 2):016210. doi: 10.1103/PhysRevE.67.016210. Epub 2003 Jan 24.
We study a system of globally coupled two-dimensional nonlinear oscillators [using the two-junction superconducting quantum interference device (SQUID) as a prototype for a single element] each of which can undergo a saddle-node bifurcation characterized by the disappearance of the stable minima in its potential energy function. This transition from fixed point solutions to spontaneous oscillations is controlled by external bias parameters, including the coupling coefficient. For the deterministic case, an extension of a center-manifold reduction, carried out earlier for the single oscillator, yields an oscillation frequency that depends on the coupling; the frequency decreases with coupling strength and/or the number of oscillators. In the presence of noise, a mean-field description leads to a nonlinear Fokker-Planck equation for the system which is investigated for experimentally realistic noise levels. Furthermore, we apply a weak external time-sinusoidal probe signal to each oscillator and use the resulting (classical) resonance to determine the underlying frequency of the noisy system. This leads to an explanation of earlier experimental results as well as the possibility of designing a more sensitive SQUID-based detection system.
我们研究了一个全局耦合的二维非线性振子系统（以双结超导量子干涉器件（SQUID）作为单个元件的原型），其中每个振子都可能经历鞍结分岔，其特征是势能函数中稳定极小值的消失。从定点解到自发振荡的这种转变由外部偏置参数控制，包括耦合系数。对于确定性情况，早期对单个振子进行的中心流形约化的扩展，得到了一个依赖于耦合的振荡频率；频率随耦合强度和/或振子数量的增加而降低。在存在噪声的情况下，平均场描述导致了一个针对该系统的非线性福克 - 普朗克方程，我们针对实验现实的噪声水平对其进行了研究。此外，我们向每个振子施加一个弱的外部时间正弦探测信号，并利用由此产生的（经典）共振来确定有噪声系统的潜在频率。这导致了对早期实验结果的解释，以及设计一个更灵敏的基于SQUID的检测系统的可能性。
