A chaotic system in synchronization and secure communications

In this paper we deal with the synchronization and parameter estimations of an uncertain Rikitake system and its application in secure communications employing chaotic parameter modulation. The strategy consists of proposing a receiver system which tends to follow asymptotically the unknown Rikitake system, refereed as transmitter system. The gains of the receiver system are adjusted continually according to a convenient high order sliding-mode adaptative controller (HOSMAC), until the measurable output errors converge to zero. By using HOSMAC, synchronization between transmitter and receiver is achieved and message signals are recovered. The convergence analysis is carried out by using Barbalat's Lemma.