Enhancing synchronism of chaotic systems

Recent work has considered the situation where a state variable (or variables) of a chaotically evolving system is used as an input to a replica of part of the original system. It was found that the replica subsystem often synchronizes to the chaotic evolution of the original system, and it has been suggested that this phenomenon may be used for secure communications. In this paper we point out that exact synchronism may also occur for a large class of systems that are not replicas of part of the original system. This allows greater freedom in choosing synchronizer systems, and we discuss the possibility of using this freedom to choose synchronizer systems with improved performance. Two explicit examples illustrating this statement are given, one where the chaotic system consists of three autonomous differential equations, and the other where the chaotic system is a two-dimensional map.