Efficient algorithm for detecting unstable periodic orbits in chaotic systems

Details Efficient algorithm for detecting unstable periodic orbits in chaotic systems Efficient algorithm for detecting unstable periodic orbits in chaotic systems

1999-06-03

arxiv.org/abs/chao-dyn/9906007v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, 3 figures, 1 table, submitted to PRE as Rapid Communication

Scientific paper

10.1103/PhysRevE.60.6172

We present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of a new iterative scheme and an effective technique for selecting initial points. The iterative scheme is based on the semi-implicit Euler method, which has both fast and global convergence, and only a small number of initial points is sufficient to detect all unstable periodic orbits of a given period. The power of our method is illustrated by numerical examples of both two- and four-dimensional maps.

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