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Transition to chaos in a fluid motion system

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  • Chen, Zhi-Min
  • Price, W.G.

Abstract

To provide a mathematical description of the chaotic behaviour in a fluid flow, a coupled system of seven ordinary differential equations is truncated from the Navier–Stokes equations in a plane domain. This truncation system shows a route to low-dimensional chaos through a Hopf bifurcation and a sequence of global bifurcations including periodic doubling.

Suggested Citation

  • Chen, Zhi-Min & Price, W.G., 2005. "Transition to chaos in a fluid motion system," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1195-1202.
  • Handle: RePEc:eee:chsofr:v:26:y:2005:i:4:p:1195-1202
    DOI: 10.1016/j.chaos.2005.02.045
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    Cited by:

    1. Nejib Smaoui, 2018. "Symmetries, Dynamics, and Control for the 2D Kolmogorov Flow," Complexity, Hindawi, vol. 2018, pages 1-15, May.
    2. Xu, Mingtian, 2007. "Property of period-doubling bifurcation cascades of discrete dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 455-462.
    3. Gambino, G. & Lombardo, M.C. & Sammartino, M., 2009. "Adaptive control of a seven mode truncation of the Kolmogorov flow with drag," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 47-59.
    4. Chen, Zhi-Min & Price, W.G., 2006. "Transition to a pair of chaotic symmetric flows," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1285-1291.

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