Effect of Network Size on Collective Motion of Mean Field for a Globally Coupled Map with Disorder

We investigate the effect of the network size (or the elements number) on the collective motion of the mean field for a globally coupled map with disorder. It is shown that, with the increasing network size, the collective motion of the mean field of the globally coupled map can be shrunk periodically. In the absence of disorder or in the presence of disorder while without the coupling, this phenomenon is absent. Our result means that disorder can make the globally coupled map tame itself for certain numbers of network size. In addition, we discuss the possible application of our result to the network for action potential wave block at-a-distance in the heart.