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Dynamical study of quadrating harvesting of a predator–prey model with Monod–Haldane functional response

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Abstract

In this study, we have investigated local and global dynamics of a modified Leslie–Gower predator–prey model with Monod–Haldane functional response, where prey is subjected to quadratic harvesting. It is found that the solutions of the proposed system are positive and bounded uniformly. The feasible equilibrium points are also obtained for some suitable and predefined conditions. It is observed that the system exhibits at most three non-zero interior equilibrium points for different choices of parameters under certain conditions. The dynamics of all these feasible equilibrium points have been analysed using Routh–Hurwitz criterion. Local bifurcations analysis such as transcritical and saddle-node bifurcations have been investigated using Sotomayor’s theorem. To demonstrate the analytical results, numerical simulations using some suitable data set are carried out. Optimal harvesting policy has been obtained using Pontryagin’s Maximum Principle to show that the species can be preserved from extinction and a sustainable fishery can be achieved.

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Authors and Affiliations

  1. Department of Applied Sciences, Chandigarh Group of Colleges, Landran, Mohali, Punjab, India

    Manpreet Kaur

  2. Department of Mathematics, School of Advanced Sciences, VIT University, Vellore, Tamilnadu, India

    Reenu Rani & Rachna Bhatia

  3. Department of Mathematics, S.S.I.E.T., Dera Bassi, Zirakpur, Punjab, India

    Govinder Nath Verma

  4. Centre for Biomaterials, Cellular and Molecular Theranostics, VIT University, Vellore, Tamilnadu, India

    Satyaprakash Ahirwar

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  1. Manpreet Kaur
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  2. Reenu Rani
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  4. Govinder Nath Verma
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  5. Satyaprakash Ahirwar
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Correspondence to Reenu Rani.

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Kaur, M., Rani, R., Bhatia, R. et al. Dynamical study of quadrating harvesting of a predator–prey model with Monod–Haldane functional response. J. Appl. Math. Comput. 66, 397–422 (2021). https://doi.org/10.1007/s12190-020-01438-0

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