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