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arXiv · 1608.08442

Reverse-engineering invariant manifolds with asymptotic phase

Matthew Kvalheim·Shai Revzen
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Abstract

We present a recipe for rendering a submanifold normally hyperbolic and invariant within a stability basin. The construction includes the ability to choose the asymptotic phase map. We are motivated by the notion of "templates and anchors" -- the biomechanical observation that animal motions are often governed by low dimensional dynamics -- and the growing applications in robotics which desire means for making such biologically derived templates govern the dynamics of robots. Our approach is fairly universal, in the sense that a broad range of model reduction constructions must be normally hyperbolic if they are robust, and a broad range of such normally hyperbolic systems can be produces from our construction.

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Matthew Kvalheim, Shai Revzen. 2016-08-30. Reverse-engineering invariant manifolds with asymptotic phase. https://arxiv.org/abs/1608.08442

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