Propagation of projective synchronization in a series connection of chaotic systems

Abstract

Projective synchronization is a type of chaos synchronization where the response system states are scaled replicas of the drive system states. This paper deals with the propagation of projective synchronization in a series connection of N chaotic discrete-time drive systems and N response systems. By exploiting an observer-based approach, the paper demonstrates that dead-beat projective synchronization (i.e., exact synchronization in finite time for any scaling factor) is achieved between the n th drive and n th response systems. In particular, it is shown that projective synchronization starts from the innermost ( N th) drive–response system pair and propagates toward the outermost (first) drive–response system pair. Only a single scalar synchronizing signal connects the cascaded drive and response systems. Finally, an example illustrates the propagation of different types of chaos synchronization in a series connection consisting of a Gingerbreadman map, a third order hyperchaotic Henon map and a Lozi map.