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Spatiotemporal Dynamics of Fractional Predator–Prey System with Stage Structure for the Predator

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Abstract

In this paper, pseudo-spectral method have been proposed as an efficient and easy to adapt method for solving the space fractional reaction–diffusion system. We have studied a fractional predator–prey system where the predator has a life history that takes through the immature and mature stages. Sufficient feasible conditions are obtained for the global asymptotic of the equilibrium state of the system. The main advantage of this approach is that it gives a full diagonal representation of the fractional operator, being able to achieve spectral convergence regardless of the fractional power in the problem. Additional advantage is that the application of the proposed method to two and three spatial dimensions requires a straightforward extension to the one dimensional case. Numerical simulation results of the space fractional reaction–diffusion system, especially in two and three dimensions provide some amazing dynamics when compared to the classical reaction-diffusion equation, and as such consider as a powerful modelling approach for understanding the various aspects of heterogeneity in excitable media. Numerical experiments justify that the results obtained by the proposed method agree well with the theoretical findings.

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Acknowledgements

The authors are grateful to both the academic editor and anonymous referees for their suggestions and useful comments on this paper.

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Authors and Affiliations

  1. Faculty of Natural and Agricultural Sciences, Institute for Groundwater Studies, University of the Free State, Bloemfontein, 9300, South Africa

    Kolade M. Owolabi & Abdon Atangana

  2. Department of Mathematical Sciences, Federal University of Technology, Akure, PMB 704, Ondo State, Nigeria

    Kolade M. Owolabi

Authors
  1. Kolade M. Owolabi
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  2. Abdon Atangana
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Correspondence to Kolade M. Owolabi.

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Owolabi, K.M., Atangana, A. Spatiotemporal Dynamics of Fractional Predator–Prey System with Stage Structure for the Predator. Int. J. Appl. Comput. Math 3 (Suppl 1), 903–924 (2017). https://doi.org/10.1007/s40819-017-0389-2

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  • DOI: https://doi.org/10.1007/s40819-017-0389-2

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