Synchronizing multiple chaotic maps with a randomized scalar coupling

Synchronization between chaotic systems has recently been a topic of great interest among physicists and engineers. In addition to theoretical results, a number of applications in communications and control have also been proposed. We have previously shown that identical chaotic maps can, under certain conditions, be synchronized by a common noise-like input. This raises the question whether the chaotic output from a map can synchronize other maps to itself. In this paper, we present results on the synchronization of two identical maps where the output of one map is used to drive both maps. We then apply this method to synchronizing identical but internally inhomogeneous populations of chaotic oscillators using a randomly constructed scalar coupling signal, which tends to white noise as the number of oscillators increases. Such a system may have applications in secure communication. c ©1999 Elsevier Science B.V. All rights reserved. PACS: 05.45.+b; 43.72.+q; 07.05.Pj