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Fractional-order biological system: chaos, multistability and coexisting attractors

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Abstract

In this paper, the nonlinear dynamics of the biological system modeled by the fractional incommensurate order Van der Pol equations are investigated. The stability of the proposed fractional non-autonomous system is analyzed by varying both the fractional order derivative and system parameters. Moreover, very interesting phenomena such as symmetry, multi-stability and coexistence of attractors are discovered in the considered biological system. Numerical simulations are performed by considering the Caputo fractional derivative and results are reported by means of bifurcation diagrams, computation of the largest Lyapunov exponent, phase portraits in 2D and 3D projections.

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Authors and Affiliations

  1. Laboratory of Dynamical System and Control, University of Larbi Ben M’hidi, 04000, Oum El Bouaghi, Algeria

    Nadjette Debbouche

  2. Department of Mathematics and Computer Sciences, Larbi Ben M’hidi University, Oum El Bouaghi, Algeria

    Adel Ouannas

  3. Nonlinear Dynamics Research Center (NDRC), College of Humanities and Sciences, Ajman University, Ajman, UAE

    Adel Ouannas & Shaher Momani

  4. Department of Mathematics, Faculty of Science, University of Jordan, Amman, 11942, Jordan

    Shaher Momani

  5. Department of Innovation Engineering, University of Salento, 73100, Lecce, Italy

    Donato Cafagna

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

    Viet-Thanh Pham

Authors
  1. Nadjette Debbouche
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  2. Adel Ouannas
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  3. Shaher Momani
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  4. Donato Cafagna
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  5. Viet-Thanh Pham
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Correspondence to Viet-Thanh Pham.

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Debbouche, N., Ouannas, A., Momani, S. et al. Fractional-order biological system: chaos, multistability and coexisting attractors. Eur. Phys. J. Spec. Top. 231, 1061–1070 (2022). https://doi.org/10.1140/epjs/s11734-021-00308-5

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  • DOI: https://doi.org/10.1140/epjs/s11734-021-00308-5

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