The Concept of Synchronization from the Observer's Viewpoint

Abstract

In this paper the concept of synchronization for continuous time dynamical systems from the viewpoint of an observer is considered. It is proved that: this concept is a generalization of the notion of synchronization. It is proved that the future of the points of the set in which two dynamical systems are relative probability synchronized is the same up to the homeomorphism determined by a relative probability synchronization. The persistence of relative probability synchronization under a topological conjugate relation is deduced.