On the determination of the basin of attraction of periodic orbits in three- and higher-dimensional systems |
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Authors: | Peter Giesl |
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Institution: | Department of Mathematics, Mantell Building, University of Sussex, Falmer, BN1 9RF, UK |
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Abstract: | The determination of the basin of attraction of a periodic orbit can be achieved using a Lyapunov function. A Lyapunov function can be constructed by approximation of a first-order linear PDE for the orbital derivative via meshless collocation. However, if the periodic orbit is only accessible numerically, a different method has to be used near the periodic orbit. Borg's criterion provides a method to obtain information about the basin of attraction by measuring whether adjacent solutions approach each other with respect to a Riemannian metric. Using a numerical approximation of the periodic orbit and its first variation equation, a suitable Riemannian metric is constructed. |
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Keywords: | Periodic orbit Ordinary differential equation Basin of attraction Lyapunov function Meshless collocation Radial basis function |
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