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Dynamical behaviors of fractional-order Lotka–Volterra predator–prey model and its discretization

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Abstract

In this work, we study the dynamical behaviors of fractional-order Lotka–Volterra predator–prey system and its discretized counterpart. It is shown that the discretized system exhibits much richer dynamical behaviors than its corresponding fractional-order form; in the discretized system, many types of bifurcations (transcritical, flip, Neimark–Sacker) and chaos are obtained however the dynamics of fractional-order counterpart is included only stable (unstable) equilibria. Numerical simulations are used to verify the correctness of the analytical results.

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Acknowledgments

The authors wish to thank the anonymous reviewers for providing some helpful comments which help to improve the style of this work. This research was supported by University of Hail under Grant No. SM14006.

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Authors and Affiliations

  1. Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia, 41522, Egypt

    A. A. Elsadany

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    A. A. Elsadany

  3. Mathematics Department, Faculty of Science, Hail University, Hail, 2440, Saudi Arabia

    A. E. Matouk

Authors
  1. A. A. Elsadany
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  2. A. E. Matouk
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Correspondence to A. A. Elsadany.

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Dedicated to Prof. E. Ahmed on the Occasion of his 60th Birthday.

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Elsadany, A.A., Matouk, A.E. Dynamical behaviors of fractional-order Lotka–Volterra predator–prey model and its discretization. J. Appl. Math. Comput. 49, 269–283 (2015). https://doi.org/10.1007/s12190-014-0838-6

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  • DOI: https://doi.org/10.1007/s12190-014-0838-6

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