A globally stable attractor that is locally unstable everywhere | Zendy

Phanindra Tallapragada | Zendy; Senbagaraman Sudarsanam | Zendy

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A globally stable attractor that is locally unstable everywhere

Author(s) -

Phanindra Tallapragada,

Senbagaraman Sudarsanam

Publication year - 2017

Publication title -

aip advances

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.421

H-Index - 58

ISSN - 2158-3226

DOI - 10.1063/1.5016214

Subject(s) - attractor , invariant (physics) , invariant manifold , eigenvalues and eigenvectors , manifold (fluid mechanics) , subspace topology , mathematics , fixed point , stability (learning theory) , invariant subspace , mathematical analysis , center manifold , pure mathematics , physics , computer science , mathematical physics , linear subspace , quantum mechanics , bifurcation , nonlinear system , mechanical engineering , hopf bifurcation , machine learning , engineering

We construct two examples of invariant manifolds that despite being locally unstable at every point in the transverse direction are globally stable. Using numerical simulations we show that these invariant manifolds temporarily repel nearby trajectories but act as global attractors. We formulate an explanation for such global stability in terms of the ‘rate of rotation’ of the stable and unstable eigenvectors spanning the normal subspace associated with each point of the invariant manifold. We discuss the role of this rate of rotation on the transitions between the stable and unstable regimes

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