Cooperative dynamics in a class of coupled two-dimensional oscillators

J. A. Acebrón, W.-J. Rappel, A. R. Bulsara
2003 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We study a system of globally coupled two-dimensional nonlinear oscillators ͓using the two-junction superconducting quantum interference device ͑SQUID͒ as a prototype for a single element͔ 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
more » ... ic case, an extension of a centermanifold 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 ͑classical͒ 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.
doi:10.1103/physreve.67.016210 pmid:12636588 fatcat:3gjzo6yokfcsfannv75vdzz42a