SYNCHRONIZING NONAUTONOMOUS CHAOTIC SYSTEMS WITHOUT PHASE-LOCKING

Pecora and Carroll(1) have shown how two nonautonomous chaotic circuit s driven by periodic forcing can be synchronized using the master-slav e driving principle. However, in their scheme, the periodic forcing in both circuits needs to be phase-locked through some additional circui try for the system to synchronize. In this paper, we show two ways in which this can be avoided. In the first scheme, the two circuits are c onnected in a master-slave driving configuration and the periodic forc ing is included in the driving signal such that it eliminates the need for the slave circuit to have an external periodic forcing signal. In addition, we can recover the periodic forcing signal at the slave cir cuit. In the second scheme, the two circuits are connected in a mutual coupling configuration. The two circuits will synchronize regardless of what the periodic forcing signals of the two circuits are. In parti cular, the two periodic forcing signals could have different phases, d ifferent frequencies, or different shapes. We discuss two interpretati ons of these synchronization schemes. First, we consider them as commu nication systems when the periodic forcing signal is replaced by a pro perly encoded information signal. We illustrate this in a physical cir cuit implementation. Second, we consider them as synchronization schem es for nonidentical systems by considering the external forcing signal as an error signal due to the difference between the two systems.