An Algorithm for Locating Coexisting Periodic Solutions of Nonlinear Oscillators
Wang Fuxin, Hu Haiyan
(Institute of Vibration Engineering Research, Nanjing University of Aeronautics & Astronautics 210016)

Abstract: A simple, but efficient numerical scheme is proposed to determine the coexisting periodic solutions of periodically forced nonlinear oscillators. This scheme is based upon the geometrical concept of the Poincare mapping and the theory of the singularity point of two dimensional autonomous systems. It can locate all periodic fixed points in a domain of concern and identify their types as well. The efficiency of the scheme is demonstrated through two examples in the paper.
Keywords: periodic solution, multi-attractor, Poincare mapping, cell mapping.