  Recently, the synchronization of coupled dynamical systems has been widely
studied. Synchronization is referred to as a process wherein two (or many)
dynamical systems are adjusted to a common behavior as time goes to infinity,
due to coupling or forcing. Therefore, before discussing synchronization, a
basic problem on continuation of the solution must be solved: For given initial
conditions, can the solution of coupled dynamical systems be extended to the
infinite interval $[0,+\infty)$? In this paper, we propose a general model of
coupled dynamical systems, which includes previously studied systems as special
cases, and prove that under the assumption of QUAD, the solution of the general
model exists on $[0,+\infty)$.
