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Dynamics of an additional food provided predator–prey system with prey refuge dependent on both species and constant harvest in predator

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  • Mondal, Sudeshna
  • Samanta, G.P.

Abstract

In the present work, we investigate on the dynamics of predator–prey model with prey refuge in proportion to both species and the effect of additional food provided to the predator. A Holling type II functional response in presence of additional food is taken to represent the interaction between prey and predator. Positivity and uniform boundedness of the solutions of the system are discussed analytically. Existence of equilibrium points and their stability criteria are analysed. Condition for occurrence of Hopf-bifurcation is derived analytically. It is found that the consumption rate of predator plays an important role in the dynamics of present system. Also, discrete time lag (gestation delay) in the proposed model is incorporated to observe the switching behaviour of the delay parameter through Hopf-bifurcation. Moreover, this work aims to analyse the dynamical behaviour of the considered predator–prey model when the predator is harvested at a constant rate. Numerical simulations are performed to verify all the analytical results using MATLAB and MATCONT.

Suggested Citation

  • Mondal, Sudeshna & Samanta, G.P., 2019. "Dynamics of an additional food provided predator–prey system with prey refuge dependent on both species and constant harvest in predator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    • Handle: RePEc:eee:phsmap:v:534:y:2019:i:c:s0378437119313317
    DOI: 10.1016/j.physa.2019.122301
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    References listed on IDEAS

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    1. Das, Amartya & Samanta, G.P., 2018. "Stochastic prey–predator model with additional food for predator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 121-141.
    2. Sen, Moitri & Srinivasu, P.D.N. & Banerjee, Malay, 2015. "Global dynamics of an additional food provided predator–prey system with constant harvest in predators," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 193-211.
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    Citations

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    Cited by:

    1. Das, Amartya & Samanta, G.P., 2020. "A prey–predator model with refuge for prey and additional food for predator in a fluctuating environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    2. Yang, Yafei & Fan, Meng, 2023. "Impact of selective grazing on the dynamics of a diffusive plankton model with component Allee effect and additional food," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Mandal, Saroj Kumar & Poria, Swarup, 2023. "A study of Michaelis–Menten type harvesting effects on a population in stochastic environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    4. Das, Meghadri & Samanta, G.P., 2020. "A delayed fractional order food chain model with fear effect and prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 218-245.
    5. Mondal, Sudeshna & Samanta, Guruprasad, 2022. "Dynamics of a delayed toxin producing plankton model with variable search rate of zooplankton," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 166-191.

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