A lattice refinement scheme for finding periodic orbits

B.I. Henry, S.D. Watt, S.L. Wearne

Abstract


A lattice refinement scheme based on the principle of linearized stability is introduced to locate periodic orbits in a two-dimensional map. The method locates all periodic orbits of a specified order within a given starting window and it can be equally well applied when the map is only known implicitly, e.g., as a two-dimensional surface of section arising from a three-dimensional flow. Periodic orbits in the Henon Map, the Predator-Prey Map, the Rossler Flow, and the Lorenz Flow are constructed as illustrations of the method.

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DOI: http://dx.doi.org/10.21914/anziamj.v42i0.619



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.