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arXiv · 1308.1165

Nonautonomous control of stable and unstable manifolds in two-dimensional flows

Sanjeeva Balasuriya·Kathrin Padberg-Gehle
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Abstract

We outline a method for controlling the location of stable and unstable manifolds in the following sense. From a known location of the stable and unstable manifolds in a steady two-dimensional flow, the primary segments of the manifolds are to be moved to a user-specified time-varying location which is near the steady location. We determine the nonautonomous perturbation to the vector field required to achieve this control, and give a theoretical bound for the error in the manifolds resulting from applying this control. The efficacy of the control strategy is illustrated via a numerical example.

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Sanjeeva Balasuriya, Kathrin Padberg-Gehle. 2013-08-06. Nonautonomous control of stable and unstable manifolds in two-dimensional flows. https://doi.org/10.1016/j.physd.2014.03.003

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