Electron. J. Diff. Eqns., Vol. 2003(2003), No. 39, pp. 1-10.

Synchronization of nonautonomous dynamical systems

Peter E. Kloeden

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

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P. E. Kloeden
Fachbereich Mathematik
Johann Wolfgang Goethe Universitat
D-60054 Frankfurt am Main, Germany
e-mail: kloeden@math.uni-frankfurt.de

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