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New approach for stability and bifurcation analysis on predator–prey harvesting model for interval biological parameters with time delays

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Abstract

This paper presents a prey–predator harvesting model with time delay for bifurcation analysis. We consider the parameters of the proposed model with imprecise data as form of interval in nature, due to the lack of precise numerical information of the biological parameters such as prey population growth rate and predator population decay rate. The interaction between prey and predator is assumed to be governed by a Holling type II functional response and discrete type gestation delay of the predator for consumption of the prey under impreciseness of the biological parameters. Parametric functional form of interval number with two parameters is introduced. This study reveals that not only delay and harvesting effort play a significant role on the stability on the system but also interval parameters play a crucial role on the stability of the system. Computer simulations of numerical examples are given to explain our proposed imprecise model. We also address critically the biological implications of our analytical findings with proper numerical example.

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Acknowledgements

The authors are grateful to the anonymous referees, Editor-in-Chief (Jose E. Souza de Cursi) and Associate Editor (Luz de Tereza) for their careful reading, valuable comments and helpful suggestions, which have helped the authors to improve the presentation of this work significantly.

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Authors and Affiliations

  1. Chandrahati Dilip Kumar High School (H.S.), Chandrahati, West Bengal, 712504, India

    D. Pal

  2. Department of Mathematics, National Institute of Technology Puducherry, Karaikal, 609605, India

    G. S. Mahapatra

  3. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103, India

    G. P. Samanta

Authors
  1. D. Pal
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  2. G. S. Mahapatra
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  3. G. P. Samanta
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Correspondence to D. Pal.

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Communicated by Luz de Teresa.

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Pal, D., Mahapatra, G.S. & Samanta, G.P. New approach for stability and bifurcation analysis on predator–prey harvesting model for interval biological parameters with time delays. Comp. Appl. Math. 37, 3145–3171 (2018). https://doi.org/10.1007/s40314-017-0504-3

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  • DOI: https://doi.org/10.1007/s40314-017-0504-3

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