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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 14, issue 5
Nonlin. Processes Geophys., 14, 615–620, 2007
https://doi.org/10.5194/npg-14-615-2007
© Author(s) 2007. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Special issue: Nonlinear waves and turbulence in space

Nonlin. Processes Geophys., 14, 615–620, 2007
https://doi.org/10.5194/npg-14-615-2007
© Author(s) 2007. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  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.

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