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Bifurcation and chaos in the fractional form of Hénon-Lozi type map

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Abstract

In this paper, we are particularly interested in the fractional form of the Hénon-Lozi type map. Using discrete fractional calculus, we show that the general behavior of the proposed fractional order map depends on the fractional order. The dynamical properties of the new generalized map are investigated by applying numerical tools such as: phase portrait, bifurcation diagram, largest Lyapunov exponent, and 0-1 test. It shows that the fractional order Hénon-Lozi map exhibits a range of different dynamical behaviors including chaos and coexisting attractors. Furthermore, a one-dimensional control law is proposed to stabilize the states of the fractional order map. Numerical results are presented to illustrate the findings.

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Authors and Affiliations

  1. Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Larbi Tebessi, Tebessa, 12002, Algeria

    Adel Ouannas

  2. College of Humanities and Sciences, Ajman University, Ajman, UAE

    Adel Ouannas & Shaher Momani

  3. Laboratory of dynamical systems and control, University of Larbi Ben M’hidi, Oum El Bouaghi, Algeria

    Amina–Aicha Khennaoui

  4. Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong 518060, P.R. China

    Xiong Wang

  5. Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Viet-Thanh Pham

  6. Department of Mathematics, College of Sciences and Arts, Al-Rass, Qassim University, Buraydah, Kingdom of Saudi Arabia

    Salah Boulaaras

  7. Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran 1, Ahmed Benbella, Oran, Algeria

    Salah Boulaaras

  8. Department of Mathematics, Faculty of Science, The University of Jordan, Amman, Jordan

    Shaher Momani

  9. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia

    Shaher Momani

Authors
  1. Adel Ouannas
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  2. Amina–Aicha Khennaoui
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  3. Xiong Wang
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  4. Viet-Thanh Pham
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  5. Salah Boulaaras
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  6. Shaher Momani
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Corresponding author

Correspondence to Viet-Thanh Pham.

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Ouannas, A., Khennaoui, A., Wang, X. et al. Bifurcation and chaos in the fractional form of Hénon-Lozi type map. Eur. Phys. J. Spec. Top. 229, 2261–2273 (2020). https://doi.org/10.1140/epjst/e2020-900193-4

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