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

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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.

Original languageEnglish
JournalPhysica D: Nonlinear Phenomena
Volume276
Pages (from-to)48-60
Number of pages13
ISSN0167-2789
DOIs
Publication statusPublished - 15.05.2014
Externally publishedYes

    Research areas

  • Controlling invariant manifolds, Flow barriers, Nonautonomous flow
  • Mathematics

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