Equilibria, periodic orbits and computing them

Ashley P. Willis

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arXiv · 1908.06730

Equilibria, periodic orbits and computing them

Ashley P. Willis

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Abstract

In this short exposition, we describe equilibria and periodic orbits in terms of the flow map, {\Phi}, and discuss the essentials of the Jacobian-free Newton-Krylov (JFNK) method that can be used to find them. This method requires little more than calls to an existing time stepping code, which {\Phi} can be considered to represent. Fortran90 / MATLAB code is available to try it out for yourself, where, in the template/example the method is applied to the Lorenz system. This code is problem-independent and can be applied to large systems, having initially been developed to find periodic orbits in simulations of pipe flow.

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Ashley P. Willis. 2019-08-09. Equilibria, periodic orbits and computing them. https://arxiv.org/abs/1908.06730

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