We present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of an 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.
|Number of pages
|Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|Published - 1999
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics