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Effect of delay and control on a predator–prey ecosystem with generalist predator and group defence in the prey species

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Abstract

Generalist predators consist an important component of an ecosystem which may act as a biocontrol agent and influence the dynamics significantly. In this paper, we have studied the effect of delayed logistic growth of the prey species with group defence behaviour. The Lyapunov stability criteria for the interior equilibrium point is derived. Also, the condition of Hopf bifurcation and the point of bifurcation are obtained. The length of the delay is also estimated for the system to preserve stability. Numerical simulations are performed and illustrated to support the obtained analytical results. Using a feedback control mechanism, the stability of the unstable equilibrium point is restored. Latin hypercube sampling/partial rank correlation coefficient (LHS/PRCC) sensitivity analysis, which is an efficient tool often employed in uncertainty analysis, is used to explore the entire parameter space of a model.

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Acknowledgements

We are very much thankful to the anonymous reviewers for their insightful comments and suggestions, which helped us to improve the manuscript considerably and further open doors for future work.

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Authors and Affiliations

  1. Department of Mathematics, NIT Durgapur, Durgapur, 713209, India

    Rajesh Ranjan Patra & Sarit Maitra

  2. Department of Mathematics, Faculty of Science and Technology, ICFAI University Tripura, Kamalghat, Mohanpur, West Tripura, 799210, India

    Soumen Kundu

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  1. Rajesh Ranjan Patra
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Patra, R.R., Kundu, S. & Maitra, S. Effect of delay and control on a predator–prey ecosystem with generalist predator and group defence in the prey species. Eur. Phys. J. Plus 137, 28 (2022). https://doi.org/10.1140/epjp/s13360-021-02225-x

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