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Dynamical analysis of a fractional-order predator–prey model incorporating a constant prey refuge and nonlinear incident rate

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Abstract

In this work, we have formulated and analyzed a fractional-order predator–prey model with an asymptotic incidence rate and constant prey refuge. Due to vulnerability, it is assumed that predator consumes only infected prey. Our mathematical formulation of the non-integer-order initial value problem has been developed on the famous fractional-order Caputo derivative. The main objective of this work is to investigate the influence of fractional-order derivatives on the system over the classical integer-order model. We have discussed the existence of non-negative solution, uniqueness and boundedness of our considered model. Analysis of local stability and Hopf bifurcation are performed both analytically and numerically. Sufficient conditions are established to guarantee the global stability of the interior equilibrium point by constructing a suitable Lyapunov function. Finally, some numerical simulations are provided to validate our results.

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Acknowledgements

The authors are grateful to the Editor and anonymous reviewers for their helpful comments and suggestions for improving the paper.

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  1. Department of Mathematics, Vivekananda College, Thakurpukur, Kolkata, 700063, India

    Chandan Maji

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  1. Chandan Maji
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Maji, C. Dynamical analysis of a fractional-order predator–prey model incorporating a constant prey refuge and nonlinear incident rate. Model. Earth Syst. Environ. 8, 47–57 (2022). https://doi.org/10.1007/s40808-020-01061-9

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