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Dynamic Analysis of a Fractional Map with Hidden Attractor

  • Amina Aicha Khennaoui
  • Adel Ouannas
  • Giuseppe Grassi
  • Ahmad Taher AzarEmail author
Conference paper
  • 162 Downloads
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1153)

Abstract

In this paper, a novel three dimensional fractional-order map is proposed. This fractional map has no fixed point, but it can also exhibit rich and complex dynamical behavior. The dynamical properties of the new model are investigated by applying numerical tools such as bifurcation diagram, maximum Lyapunov exponent, phase portraits, and evolution of states. It shows that the fractional order map is more complex when the fractional order is small.

Keywords

Chaos Bifurcation diagram Discrete fractional calculus Hidden attractors Lyapunov exponent 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Amina Aicha Khennaoui
    • 1
  • Adel Ouannas
    • 2
  • Giuseppe Grassi
    • 3
  • Ahmad Taher Azar
    • 4
    • 5
    Email author
  1. 1.Department of Mathematics and Computer SciencesUniversity of Larbi Ben M’hidiOum El BouaghiAlgeria
  2. 2.LAMIS Laboratory, Department of MathematicsUniversity of Larbi TebessiTebessaAlgeria
  3. 3.Dipartimento Ingegneria InnovazioneUniversità del SalentoLecceItaly
  4. 4.Robotics and Internet-of-Things Lab (RIOTU)Prince Sultan UniversityRiyadhSaudi Arabia
  5. 5.Faculty of Computers and Artificial IntelligenceBenha UniversityBenhaEgypt

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