In [CNSNS 16, 2845 (2011)] we propose a method which extends this basin of attraction of standard Newton-based methods to determine periodic orbits by use of systematized trial and error converging procedure. In order to do that, we combine a deterministic algorithm with a Simulated Annealing algorithm to approximate the periodic orbits. In other words, the goal of this stochastic method is to enable the determination of initial guesses with sufficient accuracy to lay them into the basin of attraction of a fast converging algorithm like the Newton-Raphson algorithm. As a consequence of the underlying stochastic nature of the algorithm, it enables one to determine several different periodic orbits for the considered dynamical system by launching the algorithm several times.
The present program corresponds to the algorithm presented and used in the reference. The function "SA_He_PO.m" serves as a test case to illustrate the feasibility of the method and the success of the algorithm in finding periodic orbits. The considered example describes a two degree of freedom atomic model.
Mauger François (2020). Simulated annealing algorithm for finding periodic orbits (https://www.mathworks.com/matlabcentral/fileexchange/35345-simulated-annealing-algorithm-for-finding-periodic-orbits), MATLAB Central File Exchange. Retrieved .