Synchronization between variable time-delayed systems and cryptography

In this letter we consider the phenomena of chaos synchronization for time-delayed dynamical systems when the delay is not constant. As an example we have considered the autonomous continuous-time-delayed system studied by Ucar, when the delay is modulated. The region in the parameter space for the onset of chaos is explored and both analytical and numerical methodologies are used for the analysis of the synchronization of two such systems, using the Krasovskii-Lyapunov functional. We have applied the adaptive coupling method for synchronization and studied the implementation of cryptography for this coupled system. The message extraction procedure is illustrated with the help of simulated results.