Articles | Volume 14, issue 5
Nonlin. Processes Geophys., 14, 615–620, 2007
https://doi.org/10.5194/npg-14-615-2007

Special issue: Nonlinear waves and turbulence in space

Nonlin. Processes Geophys., 14, 615–620, 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 Y. Saiki
  • 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.