Hidetaka ITO, Yusuke MOCHIDA, Akira KUMAMOTO
Department of Electrical and Electronic Engineering, Kansai University, Osaka, Japan
Abstract—We present a numerical method for efficiently detecting unstable periodic orbits (UPO's) embedded in chaotic attractors of high-dimensional systems. This method, which we refer to as subspace fixed-point iteration, locates fixed points of Poincaré maps using a form of fixed-point iteration that splits the phase space into appropriate subspaces. In this paper, among a number of possible implementations, we primarily focus on a subspace method based on the Schmelcher-Diakonos (SD) method that selectively locates UPO's by varying a stabilizing matrix, and present some applications of the resulting subspace SD method to hyperchaotic attractors where the UPO's have more than one unstable direction.
Keywords—nonlinear dynamics; chaos; unstable periodic orbits; numerical analysis; subspaces
Manuscript Number: 1674-8042(2010)supp.-0053-04
dio: 10.3969/j.issn1674-8042.2010.supp..14
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