Approach to the stabilization of unstable periodic solutions of autonomous systems of partial differential equations |
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Authors: | A D Dubrovskiy |
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Institution: | 1.European Organization for Nuclear Research (CERN),Genève,Switzerland |
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Abstract: | We suggest an approach to the stabilization of unstable periodic solutions of autonomous systems of partial differential equations
based on the introduction of a derivative system in which each periodic solution of the original system is stationary. By
using the introduction of an additional space into the derivative system, we suggest to stabilize its stationary solution
corresponding to a periodic solution of the original system. This approach permits effectively obtaining a complete ordered
set of functions corresponding to an unstable cycle of the original system. We consider an example of stabilization of an
unstable cycle in the Kuramoto-Tsuzuki system. |
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