CRITICAL SCALING BEHAVIOR IN COUPLED MAGNETIC OSCILLATORS

Abstract

We study the critical scaling behaviors of period doublings in N (N=2,3,4,…) coupled magnetic oscillators by varying the driving amplitude A and the coupling strength c. It is found that the critical scaling behaviors depend on the range of coupling. For the extreme long-range case of global coupling, the critical set (set of critical points) is composed of the zero-coupling critical point with c=0 and an infinity of critical line segments in the A-c plane, independently of N. Three kinds of critical scaling behaviors are found on the critical set. However, for any other nonglobal-coupling cases of shorter-range couplings, the structure of the critical set becomes different from that for the global-coupling case, because of a significant change in the stability diagram. We also note that the structure of the critical set and the critical scaling behaviors for both cases of the global and nonglobal couplings are the same as those in the abstract system of the coupled one-dimensional maps.