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Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium. (English) Zbl 1340.34180

Summary: An abstract theory on general synchronization of a system of several oscillators coupled by a medium is given. By generalized synchronization we mean the existence of an invariant manifold that allows a reduction of the dimension. The case of a concrete system modeling the dynamics of a chemical solution on two containers connected to a third container is studied. Conditions under which synchronization occurs are given. Our theoretical results are complemented with a numerical study.

MSC:

34D06 Synchronization of solutions to ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
37C60 Nonautonomous smooth dynamical systems
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References:

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