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An improvement on Marotto’s theorem and its applications to chaotification of switching systems

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  • Zhao, Yi
  • Xie, Lingli
  • Yiu, K.F. Cedric

Abstract

The controversy surrounding the correctness of Marotto’s theorem continues over the last two decades, with many researchers claiming to have found an error in the proof. In this paper, we show that Marotto’s theorem is indeed correct for analyzing the existence of chaos in the sense of Li-Yorke even after relaxing certain assumptions in the proof. In addition, we extend the theory to derive the conditions for the existence of chaos in the sense of Devaney. We show that these results can be applied to study the chaotification of linear switching systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:5:p:2225-2232
    DOI: 10.1016/j.chaos.2007.06.109
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    References listed on IDEAS

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    1. Marotto, F.R., 2005. "On redefining a snap-back repeller," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 25-28.
    2. Liu, Xinzhi & Teo, Kok-Lay & Zhang, Hongtao & Chen, Guanrong, 2006. "Switching control of linear systems for generating chaos," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 725-733.
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