Nonsimultaneity effects in globally coupled maps

Abstract

We study the behavior of globally coupled maps when the coupling mean field is either delayed or averaged over several time steps. We find that introducing a delay does not reduce, and in some cases increases, the saturation values for the fluctuations of the mean field. The mean field changes its quasiperiodic behavior by introducing more components in its spectrum, and the distance between main components of this spectrum is reduced in a linear way. On the other hand, averaging the mean field reduces the saturation value for fluctuations, but does not fully restore statistical behavior to the system except in the limit of very large averages. As before, quasiperiodicity is changed by the introduction of more beating frequencies, and the distance between the most important among them decreases linearly. As an extra test, we study the effects that a small periodic driving has over this dynamics, and find that although there is some influence, there are not strong resonances to simple sinusoidal driving.