Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 39, pp. 1-10.

Title: Synchronization of nonautonomous dynamical systems

Author: Peter E. Kloeden (Johann Wolfgang Goethe Univ., Germany)

Abstract: 
  The synchronization of two nonautonomous dynamical systems
  is considered, where the systems are described in terms of
  a skew-product formalism, i. e., in which an inputed autonomous
  driving system governs the evolution of the vector field of a
  differential equation with the passage of time.  It is shown that the 
  coupled trajectories converge to each other as time increases for 
  sufficiently large coupling coefficient and also that the component 
  sets of the pullback attractor of the coupled system converges upper 
  semi continuously as the coupling parameter increases to the diagonal of
  the product of the corresponding component sets of the pullback
  attractor of a system generated by the average of the vector fields of
  the original uncoupled systems.
 
Submitted January 30, 2003.  Published April 11, 2003.
Math Subject Classifications: 37B55, 34D45
Key Words: Nonautonomous semidynamical system; skew-product semi-flow;  
           pullback attractor; synchronization