On the Tongue-Like Bifurcation Structures of the Mean-Field Dynamics in a Network of Chaotic Elements

Abstract

Collective behavior is studied in globally coupled maps. Several coherent motions exist, even in fully desynchronized state. To characterize the collective behavior, we introduce scaling transformation of parameter, and detect the tongue-like structure of collective motions in parameter space. Such collective motion is supported by the separation of time scale, given by the self-consistent relationship between the collective motion and chaotic dynamics of each element. It is shown that the change of collective motion is related with the window structure of a single one-dimensional map. Formation and collapse of regular collective motion are understood as the internal bifurcation structure. Coexistence of multiple attractors with different collective behaviors is also found in fully desynchronized state. 05.45+b,05.90+m,87.10+e Keywords: Globally coupled map, Mean field dynamics, Collective motionComment: 45 pages + 32 figures, submitted to Physica