From collective oscillations to collective chaos in a globally coupled oscillator system
It seems that scientists' attention is attracted by collective behaviors of a large population of densely interconnected oscillators in recent years. The authors study the case of globally coupled Ginzburg-Landau oscillators. The authors make several assumptions in order to simplify their study and to extract precious conclusions for qualitative interpretation. One of the most important properties is the one of all-to-all coupled systems: each oscillator couples to all the others with identical strength. For this particular type of global coupling the individual motion of the oscillators and the behavior of the internal field which drives the oscillators are interrelated in an exact self-consistent manner. Although there are some existing studies which take account of amplitude degree of freedom, it is not always clear which features of the collective behaviors obtained depend essentially on the presence of this degree of freedom. The authors successfully proceed to find new dynamical features which are absent in those models without amplitude degree of freedom by employing an idealized amplitude model which reduces in a certain limit to the well-known phase model.
scientific article; zbMATH DE number 951923
scientific article