FROM COLLECTIVE OSCILLATIONS TO COLLECTIVE CHAOS IN A GLOBALLY COUPLED OSCILLATOR SYSTEM

Various types of collective behaviors are discovered in globally coupled Ginzburg-Landau oscillators. When the coupling is sufficiently weak, the oscillators are either in complete synchrony or their phases are scattered completely randomly. For finite coupling, new collective behaviors emerge such as splitting of the population into a small number of clusters or their fusion into a continuous stringlike distribution in the phase plane. Low-dimensional chaotic dynamics arises from the coupled motion of 3 point-clusters. Chaotic motion is also exhibited by fused clusters which is of extremely high dimension possibly proportional to the system size as is implied from its Lyapunov analysis. In the latter type of chaos, the motion of the string is in some cases characterized by repeated stretching-and-foldings. It is argued how this kind of coherent behavior seen on a collective level does not contradict the high dimensionality of the corresponding chaotic attractor.