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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Complex Dynamics of a Prey-predator System Incorporating Functional Response Dependent Prey Refuge with Harvesting

Journal of Applied Nonlinear Dynamics 10(3) (2021) 493--512 | DOI:10.5890/JAND.2021.09.010

Soovoojeet Jana$^1$ , Srabani Guria$^2$, Abhijit Ghorai$^3$, Tapan Kumar Kar$^4$

$^1$ Department of Mathematics, Ramsaday College, Amta-711401, Howrah, West Bengal, India

$^2$ Department of Mathematics, NSHM Knowledge Campus, Durgapur-713212, West Bengal, India

$^3$ Department of Mathematics, Technical University of Munich, Germany

$^4$ Department of Mathematics, IIEST, Shibpur, Howrah-711103, West Bengal, India

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Abstract

In this paper, we consider a prey-predator system allowing prey refuge and harvesting the prey species only. It is investigated under which condition the system has no limit cycle. An optimal harvesting policy is also formulated using Pontryagin's Maximum Principle. A comparison study have been done with the model in which the per individual prey refuge taken as constant. We investigate one and two parametric bifurcations thoroughly. Here we also discuss the bi-stability of the model in brief when the interior equilibrium is not unique. Some numerical simulations are given to verify our analytic works.

Acknowledgments

Research of T. K. Kar is supported by the Council of Scientific and Industrial Research(CSIR), India (File No.25(300)/19/EMR-II, dated:16th May, 2019). Moreover, the authors are very much grateful to the anonymous reviewers and the editor Albert C.J. Luo for their constructive comments and valuable suggestions to improve the quality and presentation of the manuscript significantly.

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