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Chaos in One-dimensional Piecewise Smooth Dynamical Systems

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Abstract

In this paper, we study the family of one-dimensional piecewise smooth dynamical systems in which two classic theorems are still permanent. One of them is Birkhoff transitivity theorem and the other one is Banks, Brooks, Cairns, Davis, and Stacey theorem. Baker-like maps with N-branches (N ≥ 2) constitute an open subset of this family. We show that under certain conditions, a full chaos always occurs in the family of Baker-like maps.

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The authors declare that the data supporting the findings of this study are available within the article.

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Acknowledgements

The second author would like to thank the assistance of Iran National Science Foundation (INSF) and Shahid Bahonar University of Kerman in supporting the postdoc program (Project Number: 96010976).

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Authors and Affiliations

  1. Department of Mathematics, Shahid Beheshti University, Tehran, Iran

    Mehdi Pourbarat

  2. Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

    Neda Abbasi & Mohammad Reza Molaei

  3. Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

    Roya Makrooni

Authors
  1. Mehdi Pourbarat
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  2. Neda Abbasi
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  3. Roya Makrooni
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  4. Mohammad Reza Molaei
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Correspondence to Roya Makrooni.

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Pourbarat, M., Abbasi, N., Makrooni, R. et al. Chaos in One-dimensional Piecewise Smooth Dynamical Systems. J Dyn Control Syst 29, 1271–1285 (2023). https://doi.org/10.1007/s10883-022-09630-0

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  • DOI: https://doi.org/10.1007/s10883-022-09630-0

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