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Chaos and routes to chaos in coupled Duffing oscillators with multiple degrees of freedom

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  • Musielak, D.E.
  • Musielak, Z.E.
  • Benner, J.W.

Abstract

New results are reported on the routes to chaos in increasingly complex Duffing oscillator systems, which are formed by coupling several oscillators, thereby increasing the number of degrees of freedom. Other forms of increasing system complexity through distributed excitation, different forcing function phasing, different excitation frequency ratios, and higher order coupling are also studied. Changes in the quantitative aspects of the chaotic regions and in the routes to chaos of complex Duffing systems are investigated by performing numerical simulations. It is shown that the number of chaotic regions in these systems is significantly reduced when compared to the original Duffing system, and that crisis replaces period doubling as the dominant route to chaos when the number of degrees of freedom is increased. A new discovered phenomenon is that chaos emerges in the symmetrically and asymmetrically coupled Duffing oscillators only after the quasi-periodic torus breaks down through a 3-periodic and 2-periodic window, respectively.

Suggested Citation

  • Musielak, D.E. & Musielak, Z.E. & Benner, J.W., 2005. "Chaos and routes to chaos in coupled Duffing oscillators with multiple degrees of freedom," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 907-922.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:4:p:907-922
    DOI: 10.1016/j.chaos.2004.09.119
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    Cited by:

    1. El-Bassiouny, A.F., 2006. "Single-mode control and chaos of cantilever beam under primary and principal parametric excitations," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1098-1121.
    2. Bel, G. & Alexandrov, B.S. & Bishop, A.R. & Rasmussen, K.Ø., 2023. "Patterns and stability of coupled multi-stable nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Ario, Ichiro, 2013. "Multiple duffing problem in a folding structure with hill-top bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 51(C), pages 52-63.
    4. Yu, Xiang & Zhu, Shi-Jian & Liu, Shu-Yong, 2008. "Bifurcation and chaos in multi-degree-of-freedom nonlinear vibration isolation system," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1498-1504.
    5. Reis, Eduardo V.M. & Savi, Marcelo A., 2022. "Spatiotemporal chaos in a conservative Duffing-type system," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    6. El-Bassiouny, A.F., 2009. "On methods for continuous systems with quadratic, cubic and quantic nonlinearities," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1308-1316.

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