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

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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• An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems
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• Hyperbolic and Elliptic Transport Barriers in Three-Dimensional Unsteady Flows

Cited by in corpus (2)

• Local stable and unstable manifolds and their control in nonautonomous finite-time flows
• Impulsive perturbations to differential equations: stable/unstable pseudo-manifolds, heteroclinic connections, and flux