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A class of time-fractional-order continuous population models for interacting species with stability analysis

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Abstract

In recent years, prey–predator models appearing in various fields of mathematical biology have been proposed and studied extensively due to their universal existence and importance. The paper presents the solutions of time-fractional Lotka–Volterra models with the help of analytical method of nonlinear problem called homotopy perturbation method (HPM). By using initial values, the explicit solutions of time-fractional prey and predator populations for different particular cases have been derived. The numerical solutions show that only a few iterations are needed to obtain accurate approximate solutions. The dynamic behavior of the system investigated from the point of view of local stability. We also carry out a detailed analysis on stability of equilibrium.

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Acknowledgments

This research work was financially supported by BRNS of Bhabha Atomic Research Centre, Mumbai under Department of Atomic Energy, Government of India vide Grant No. 2012/37P/54/BRNS/2382.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Rourkela, 769008, India

    S. Saha Ray & S. Sahoo

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  1. S. Saha Ray
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  2. S. Sahoo
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Correspondence to S. Saha Ray.

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Saha Ray, S., Sahoo, S. A class of time-fractional-order continuous population models for interacting species with stability analysis. Neural Comput & Applic 26, 1495–1504 (2015). https://doi.org/10.1007/s00521-014-1816-5

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  • DOI: https://doi.org/10.1007/s00521-014-1816-5

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