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Stability and Bifurcation Analysis of a Discrete Prey-Predator Model with Mate-Finding Allee, Holling Type-I Functional Response and Predator Harvesting

  • General and Applied Physics
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Abstract

In this paper, we have considered a discrete-time modified Leslie-Gower type predator-prey model with mate-finding Allee, Holling Type-I functional response and predator harvesting. We have discussed the conditions of existence of the feasible equilibrium point. The stability criterion of the equilibrium point is carried out algebraically. Analytically we have shown that the system undergoes through transcritical bifurcation with respect to the rate of harvesting, period doubling bifurcation and Neimark-Sacker bifurcation considering the discretization factor (generation gap) as a bifurcation parameter. All the bifurcation phenomena have been justified numerically. Numerically we also studied the existence of 1:2, 1:3 and 1:4 response bifurcations and found the corresponding phase portrait in all the cases. Lastly, we have studied the policy of optimal harvesting maintaining the conservation of both the populations. The paper is ended with some conclusion.

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Acknowledgements

The authors would want to thank anonymous reviewers for their valuable comments and constructive suggestions for improving this manuscript.

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Author notes

  1. Susmita Sarkar and Prabir Chakraborty contributed equally to this work.

Authors and Affiliations

  1. Department of Applied Mathematics, University of Calcutta, Kolkata, 700009, West Bengal, India

    Uttam Ghosh & Susmita Sarkar

  2. Department of Mathematics, Govt. General Degree College, Muragachha, 741154, West Bengal, India

    Prabir Chakraborty

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  1. Uttam Ghosh
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  2. Susmita Sarkar
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  3. Prabir Chakraborty
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Correspondence to Prabir Chakraborty.

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Ghosh, U., Sarkar, S. & Chakraborty, P. Stability and Bifurcation Analysis of a Discrete Prey-Predator Model with Mate-Finding Allee, Holling Type-I Functional Response and Predator Harvesting. Braz J Phys 52, 190 (2022). https://doi.org/10.1007/s13538-022-01189-2

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