Dual and dual-cross synchronizations in chaotic systems

In this paper we investigate dual synchronization and dual-cross synchronization between a transmitter and a receiver, each consisting of two master and slave systems. We demonstrate our approach using the example of synchronization of chaotic external cavity laser diodes. In the synchronization scheme under consideration the joint error signal, which is the difference between the sum of the outputs from the master systems in the transmitter and the sum of outputs from the slave systems in the receiver, is fed into each slave system and synchronizations between the master lasers and slave lasers under possible configurations are studied. By use of error dynamics we derive existence conditions for synchronization between the transmitter and receiver. We find that in all the studied cases synchronization between the transmitter and receiver occurs when the sum of the contributions from individual master (or slave) systems in the transmitter (or receiver) is equal to unity. For the first time we demonstrate that an arbitrarily chosen master system from the transmitter synchronizes with the slave system from the receiver which has an equal contribution weight to the joint error signal. These findings are considered to be of interest in multichannel communication schemes. (C) 2002 Elsevier Science B.V. All rights reserved.