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Approach to the stabilization of unstable periodic solutions of autonomous systems of partial differential equations

Approach to the stabilization of unstable periodic solutions of autonomous systems of partial... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Approach to the stabilization of unstable periodic solutions of autonomous systems of partial differential equations

Dubrovskiy, A.
Differential Equations , Volume 45 (12) – Jan 21, 2010
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References (9)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Pleiades Publishing, Ltd.
Subject
Mathematics; Difference and Functional Equations; Partial Differential Equations; Ordinary Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266109120052
Publisher site
See Article on Publisher Site

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.

Journal

Differential Equations – Springer Journals

Published: Jan 21, 2010

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