Synchronization between variable time-delayed systems and cryptographyD. Ghosh1, 2, S. Banerjee2 and A. R. Chowdhury3
1 Department of Mathematics, Dinabandhu Andrews College - Goria, Calcutta - 700 084, India
2 Department of Mathematics, JIS College of Engineering, Block-A, Phase-3 - Kalyani, West Bengal, India
3 High Energy Physics Division, Department of Physics, Jadavpur University - Calcutta - 700 032, India
received 9 July 2007; accepted in final form 12 September 2007; published November 2007
published online 10 October 2007
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.
05.45.Xt - Synchronization; coupled oscillators.
05.45.Vx - Communication using chaos.
42.65.Sf - Dynamics of nonlinear optical systems; optical instabilities, optical chaos and complexity, and optical spatio-temporal dynamics.
© Europhysics Letters Association 2007