Equilibria, periodic orbits and computing them
arXiv:1908.06730
Abstract
In this short exposition, we describe equilibria and periodic orbits in terms of the flow map, Φ, 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 Φ 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.
EPSRC Summer School on Modal decompositions in fluid mechanics. DAMTP, Cambridge, 5-8 August 2019. 16 pages. (v2: references added, hyperlinks corrected)