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Synchronization of nonautonomous dynamical systems. (English) Zbl 1038.37021

Summary: 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 systems converge 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.

MSC:

37C70 Attractors and repellers of smooth dynamical systems and their topological structure
34D45 Attractors of solutions to ordinary differential equations
37B55 Topological dynamics of nonautonomous systems
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