Synchronizing nonautonomous Chaotic Systems without phase-Locking

Pecora and Carroll1 have shown how two nonautonomous chaotic circuits driven by periodic forcing can be synchronized using the master-slave driving principle. However, in their scheme, the periodic forcing in both circuits needs to be phase-locked through some additional circuitry 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 connected in a master-slave driving configuration and the periodic forcing 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 circuit. 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 particular, the two periodic forcing signals could have different phases, different frequencies, or different shapes. We discuss two interpretations of these synchronization schemes. First, we consider them as communication systems when the periodic forcing signal is replaced by a properly encoded information signal. We illustrate this in a physical circuit implementation. Second, we consider them as synchronization schemes for nonidentical systems by considering the external forcing signal as an error signal due to the difference between the two systems.