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Property of period-doubling bifurcations

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  • Wang, Liqiu
  • Xu, Mingtian

Abstract

The period-doubling bifurcation leads a T-periodic solution to a 2T-periodic solution. We develop the relation between these two periodic solutions analytically for a general parameter-dependent dynamic system. Such the relation is further confirmed by one example and shows that the 2T-periodic solution contains all the information of the T-periodic solution near the bifurcation point. Therefore we can infer the T-periodic solution from the 2T-periodic solution. Conversely, we may obtain the part of the 2T-periodic solution from the T-periodic solution. The work sheds light on the period-doubling bifurcation and chaos in general, the self-similarity of chaotic solutions in particular, forms a benchmark of numerical accuracy checking and provides new numerical schemes of period-doubling bifurcation detection.

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  • Wang, Liqiu & Xu, Mingtian, 2005. "Property of period-doubling bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 527-532.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:2:p:527-532
    DOI: 10.1016/j.chaos.2004.09.045
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    1. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
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    Cited by:

    1. Wang, Liqiu & Pang, Ophelia & Cheng, Lin, 2006. "Bifurcation and stability of forced convection in tightly coiled ducts: stability," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 991-1005.
    2. Ruzbehani, Mohsen & Zhou, Luowei & Wang, Mingyu, 2006. "Bifurcation diagram features of a dc–dc converter under current-mode control," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 205-212.
    3. Xu, Mingtian, 2007. "Property of period-doubling bifurcation cascades of discrete dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 455-462.

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