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Chaos / Volume 5 / Issue 1

Chaos 5, 271 (1995); http://dx.doi.org/10.1063/1.166076 (12 pages)

Unstable periodic orbits and templates of the Rössler system: Toward a systematic topological characterization

C. Letellier, P. Dutertre, and B. Maheu

Laboratoire d’Energétique des Systèmes et Procédés, URA CNRS 230, INSA de Rouen, BP 08, 76 130 Mont‐Saint‐Aignan, France

(Received 25 February 1994; accepted 10 August 1994)

The Rössler system has been exhaustively studied for parameter values (a∊[0.33,0.557],b=2,c=4). Periodic orbits have been systematically extracted from Poincaré maps and the following problems have been addressed: (i) all low order periodic orbits are extracted, (ii) encoding of periodic orbits by symbolic dynamics (from 2 letters up to 11 letters) is achieved, (iii) some rules of growth and of pruning of the periodic orbits population are obtained, and (iv) the templates of the attractors are elaborated to characterize the attractors topology. © 1995 American Institute of Physics.

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KEYWORDS and PACS

Keywords

DYNAMICAL SYSTEMS, PERIODIC SOLUTION, ORBITS, POINCARE MAPPING, ATTRACTORS, TOPOLOGY, CHAOTIC SYSTEMS, STABILITY, PHASE SPACE, BIFURCATION

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.166076

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

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    References

    G. Gouesbet, “Reconstruction of standard and inverse vector fields equivalent to a Rössler system,” Phys. Rev. A 44, 6264–6280 (1991).

    G. B. Mindlin, X. J. Hou, H. G. Solari, R. Gilmore, and N. B. Tufillaro, “Classification of strange attractors by integers,” Phys. Rev. Lett. 64, 2350–2353 (1990).

    C. Letellier, P. Dutertre, and G. Gouesbet, “Characterization of the Lorenz system taking into account the equivariance of the vector field,” Phys. Rev. E 49, 3492–3495 (1994).

    G. B. Mindlin, R. López-Ruiz, H. G. Solari, and R. Gilmore, “Horseshoe implications,” Phys. Rev. E 48, 4297–4304 (1993).

    T. Hall, “Weak universality in two-dimensional transitions to chaos,” Phys. Rev. Lett. 71, 58–61 (1993).

    P. Melvin and N. B. Tufillaro, “Templates and framed braids,” Phys. Rev. A 44, 3419–3422 (1991).

    L. Le Sceller, C. Letellier, and G. Gouesbet, “Algebraic evaluation of linking numbers of unstable periodic orbits in chaotic attractors,” Phys. Rev. E 49, 4693–4695 (1994).


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