Abstract
An alternative numerical method is developed to find stable and unstable periodic orbits of nonlinear dynamical systems. The method exploits the high efficiency of the Levenberg–Marquardt algorithm for medium-sized problems and has the additional advantage of being relatively simple to implement. It is also applicable to both autonomous and non-autonomous systems. As an example of its use, it is employed to find periodic orbits in the Rössler system, a coupled Rössler system, as well as an eight-dimensional model of a flexible rotor-bearing; problems which have been treated previously via two related methods. The results agree with the previous methods and are seen to be more accurate in some cases. A simple implementation of the method, written in the Python programming language, is provided as an Appendix.
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