Detecting Unstable Periodic Orbits in Hyperchaotic Systems Using Subspace Fixed-Point Iteration
نویسندگان
چکیده
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.
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