Articles | Volume 14, issue 5
https://doi.org/10.5194/npg-14-615-2007
https://doi.org/10.5194/npg-14-615-2007
14 Sep 2007
14 Sep 2007

Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors

Y. Saiki

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.