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Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors
Research Institute for Mathematical Sciences, Kyoto University, Japan
Abstract. An infinite number of unstable periodic orbits (UPOs) are embedded in a chaotic system which models some complex phenomenon. Several algorithms which extract UPOs numerically from continuous-time chaotic systems have been proposed. In this article the damped Newton-Raphson-Mees algorithm is reviewed, and some important techniques and remarks concerning the practical numerical computations are exemplified by employing the Lorenz system.
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Citation: Saiki, Y.: Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors, Nonlin. Processes Geophys., 14, 615-620, 2007. Bibtex EndNote Reference Manager
