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In order to establish chaos synchronisation with other chaotic maps, we generalize, in this study, an integer-order system proposed in 1995 to introduce a new fractional-order map. Using phase portrait, and bifurcation diagram, we establish the occurrence of chaos. The study then suggests a linear controller in order to bring two fractional-order systems into linear synchronisation. The one-dimensional and linear nature of the developed controller makes them affordable and simple to use.

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Complexities of a Two-Dimensional Discrete Fractional -Order System: Chaos and Synchronisation

  • 会议论文

  • 发表日期：

    2025年

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  • Hadjabi Fatima,
  • Mesdoui Fatiha

摘要

In order to establish chaos synchronisation with other chaotic maps, we generalize, in this study, an integer-order system proposed in 1995 to introduce a new fractional-order map. Using phase portrait, and bifurcation diagram, we establish the occurrence of chaos. The study then suggests a linear controller in order to bring two fractional-order systems into linear synchronisation. The one-dimensional and linear nature of the developed controller makes them affordable and simple to use.