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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Original Russian Text © A.D. Dubrovskiy, 2009, published in Differentsial’nye Uravneniya, 2009, Vol. 45, No. 12, pp. 1716–1722.
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Dubrovskiy, A.D. Approach to the stabilization of unstable periodic solutions of autonomous systems of partial differential equations. Diff Equat 45, 1750–1756 (2009). https://doi.org/10.1134/S0012266109120052
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DOI: https://doi.org/10.1134/S0012266109120052