Nonautonomous control of stable and unstable manifolds in two-dimensional flows
Dynamical Systems
2016-01-07 v1
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.
Keywords
Cite
@article{arxiv.1308.1165,
title = {Nonautonomous control of stable and unstable manifolds in two-dimensional flows},
author = {Sanjeeva Balasuriya and Kathrin Padberg-Gehle},
journal= {arXiv preprint arXiv:1308.1165},
year = {2016}
}