ar X iv : 0 70 8 . 42 75 v 1 [ m at h . D S ] 3 1 A ug 2 00 7 Continuation of solutions of coupled dynamical systems 1
نویسندگان
چکیده
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,+∞)? 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,+∞).
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