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The topological reconstruction of forced oscillators

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  • Solari, Hernán G.
  • Natiello, Mario A.

Abstract

Periodically forced oscillators are among the simplest dynamical systems capable to display chaos. They can be described by the variables position and velocity, together with the phase of the force. Their phase-space corresponds therefore to R2×S1. The organization of the periodic orbits can be displayed with braids having only positive crossings. Topological characterization of dynamical systems actually began to be explored in physics on this family of problems.

Suggested Citation

  • Solari, Hernán G. & Natiello, Mario A., 2009. "The topological reconstruction of forced oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2023-2034.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:2023-2034
    DOI: 10.1016/j.chaos.2009.03.167
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    References listed on IDEAS

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    1. Stavrinides, S.G. & Deliolanis, N.C. & Laopoulos, Th. & Kyprianidis, I.M. & Miliou, A.N. & Anagnostopoulos, A.N., 2008. "The intermittent behavior of a second-order non-linear non-autonomous oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1191-1199.
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    3. Chian, Abraham C.-L. & Rempel, Erico L. & Rogers, Colin, 2006. "Complex economic dynamics: Chaotic saddle, crisis and intermittency," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1194-1218.
    4. Rusinek, Rafal & Warminski, Jerzy, 2009. "Attractor reconstruction of self-excited mechanical systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 172-182.
    5. Gan, Chunbiao & He, Shimin, 2008. "Surrogate test for noise-contaminated dynamics in the Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1517-1522.
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