A general formalism for synchronization in finite dimensional dynamical systems

In this paper, an attempt is made to propose a general definition of synchronization for finite dimensional dynamical systems. The synchronization is defined here for two coupled dynamical systems with control inputs. Output functions of such systems are introduced to describe the systems’ properties on which the synchronization problem focus. Exact synchronization, asymptotic synchronization, and approximate synchronization are, respectively, defined by comparing the output functions in the corresponding ways. The definition here can also include chaos control and anti-control. The definition here covers various synchronization investigated in the references.