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Kneading theory analysis of the Duffing equation

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  • Caneco, Acilina
  • Grácio, Clara
  • Leonel Rocha, J.

Abstract

The purpose of this paper is to study the symmetry effect on the kneading theory for symmetric unimodal maps and for symmetric bimodal maps. We obtain some properties about the kneading determinant for these maps, that implies some simplifications in the usual formula to compute, explicitly, the topological entropy. As an application, we study the chaotic behaviour of the two-well Duffing equation with forcing.

Suggested Citation

  • Caneco, Acilina & Grácio, Clara & Leonel Rocha, J., 2009. "Kneading theory analysis of the Duffing equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1529-1538.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1529-1538
    DOI: 10.1016/j.chaos.2009.03.040
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    References listed on IDEAS

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    1. J. Leonel Rocha & J. Sousa Ramos, 2004. "Weighted kneading theory of one-dimensional maps with a hole," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-20, January.
    2. Wu, Xiaofeng & Cai, Jianping & Wang, Muhong, 2008. "Global chaos synchronization of the parametrically excited Duffing oscillators by linear state error feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 121-128.
    3. El Naschie, M.S., 2008. "Hierarchy of kissing numbers for exceptional Lie symmetry groups in high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 420-422.
    4. Njah, A.N. & Vincent, U.E., 2008. "Chaos synchronization between single and double wells Duffing–Van der Pol oscillators using active control," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1356-1361.
    5. Jing, Zhujun & Huang, Jicai & Deng, Jin, 2007. "Complex dynamics in three-well duffing system with two external forcings," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 795-812.
    6. El Naschie, M.S., 2008. "A derivation of the fine structure constant from the exceptional Lie group hierarchy of the micro cosmos," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 819-822.
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    Cited by:

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