Synchronization of Chaotic Systems by Means of a Nonlinear Observer: An Application to Secure Communications

Abstract

Applications of the synchronization phenomenon of dynamical systems are important in several applications as in technology and have a wealth of science. Some applications of master–slave synchronization include the control of chaos and chaotic signal masking, where several methodologies have been considered (Martínez-Guerra, Rafael, and Wen Yu, Int J Bifurcation Chaos, 18(01), pp 235–243, 2008, [1]), (Hernault, Barbot, Ouslimani, IEEE Trans Circ Syst I: Regular Papers 55, 614, 2008, [2]). Nonetheless, it has been established that synchronization of chaotic dynamical systems is not only possible but it is believed to have potential applications in communication (Mitra, Banerjee, Int J Mod Phys B 25, 521, 2011, [3]), (Saha, Banerjee, Roy Chowdhury, Phys Lett Sect A: General, Atomic Solid State Phys 326, 133, 2004, [4]). The strategy is that when is transmitted a message; it is possible to mask it with louder chaos. An outside listener only detects the chaos, which signals like meaningless noise. But if the receiver has an adequate synchronization algorithm that perfectly reproduces the chaos, the receiver can subtract off the chaotic mask and detect the original message.