Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:A3L-D

Session:

Number:211

A Visualization Method for the Stretch-and-fold Mechanism in Chaotic Dynamics

Mamoru Suefuji,  Kantaro Fujiwara,  Tohru Ikeguchi,  

pp.211-214

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.211

PDF download (800.6KB)

Methods of visualizing the stretch-and-fold mechanism in chaotic dynamical systems helps us determine whether an observed time-series is chaotic or not, and let us analyze the dynamics more precisely. We have already proposed a semi-automatic method for visualizing the stretch-and-fold mechanism, which can be applied to chaotic dynamical systems even if the structure of the chaotic dynamical systems is unknown. In this paper, we extend this method using the entropy and we show that the proposed method can detect the stretch-and-fold mechanism more clearly. We also show that the proposed method can perform accurately as the conventional method, and can be applied to a high-dimensional chaotic dynamical system and a time-series by numerical simulations.

[1] G. Robert et al, Rev. Mod. Phys., vol.70, pp.1455-1529, 1998.

[2] H. Morioka et al, Proc. IEICE Gen. Conf. '06, A-2-24, p.60, 2006.

[3] N. Lorenz et al, J. Atmos. Sci., Vol.20, pp.130-141,1963.

[a] M. Suefuji et al, Proc. IEICE Soc. Conf. '11, A-2-8, p.45, 2011.

[b] M. Suefuji et al, Proc. IEICE gen. Conf. '12, A-2-25, p.70, 2012.

[4] O. E. Rössler et al, Phy. Lett., Vol.57A, pp.397-398, 1976.

[5] F. Takens et al, Lecture Notes in Mathematics, Vol.898, pp.366-381, 1981.

[6] A. M. Fraser et al, Phy. Rev. A, Vol.33, pp.1134-1140, 1986.

[7] O. E. Rössler et al, Phy. Lett. A, Vol.71, pp.155-157, 1979.