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On redefining a snap-back repeller

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  • Marotto, F.R.

Abstract

In this note I correct a minor technical flaw in my original snap-back repeller theorem, and then discuss some recent revisions proposed by other authors that would significantly weaken the theorem.

Suggested Citation

  • Marotto, F.R., 2005. "On redefining a snap-back repeller," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 25-28.
  • Handle: RePEc:eee:chsofr:v:25:y:2005:i:1:p:25-28
    DOI: 10.1016/j.chaos.2004.10.003
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    Cited by:

    1. Tatsumi, Keiji & Obita, Yoshinori & Tanino, Tetsuzo, 2009. "Chaos generator exploiting a gradient model with sinusoidal perturbations for global optimization," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1705-1723.
    2. Chen, Shyan-Shiou & Shih, Chih-Wen, 2009. "Transiently chaotic neural networks with piecewise linear output functions," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 717-730.
    3. Dohtani, Akitaka, 2011. "Chaos resulting from nonlinear relations between different variables," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 290-297.
    4. Sun, Huijing & Cao, Hongjun, 2007. "Bifurcations and chaos of a delayed ecological model," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1383-1393.
    5. Rahman, Aminur & Blackmore, Denis, 2017. "Threshold voltage dynamics of chaotic RS flip-Flops," Chaos, Solitons & Fractals, Elsevier, vol. 103(C), pages 555-566.
    6. Li, Yan & Wang, Lidong, 2019. "Chaos in a duopoly model of technological innovation with bounded rationality based on constant conjectural variation," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 116-126.
    7. Shi, Yuming & Yu, Pei, 2006. "Study on chaos induced by turbulent maps in noncompact sets," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1165-1180.
    8. Jiang, Guirong & Yang, Qigui, 2009. "Complex dynamics in a linear impulsive system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2341-2353.
    9. Gardini, Laura & Sushko, Iryna & Avrutin, Viktor & Schanz, Michael, 2011. "Critical homoclinic orbits lead to snap-back repellers," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 433-449.
    10. Zhao, Yi & Xie, Lingli & Yiu, K.F. Cedric, 2009. "An improvement on Marotto’s theorem and its applications to chaotification of switching systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2225-2232.
    11. Gao, Yinghui, 2009. "Complex dynamics in a two-dimensional noninvertible map," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1798-1810.

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