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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

Dynamical Analysis of Delayed Predator-Prey Models and Explicit Impacts of Harvesting

Journal of Applied Nonlinear Dynamics 13(2) (2024) 373--403 | DOI:10.5890/JAND.2024.06.013

Lakpa Thendup Bhutia, Samir Biswas, Tapan Kumar Kar

Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India

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Abstract

In theoretical ecology, mathematical models are formulated to understand the interaction among species in an ecosystem. This paper explores the dynamics of three predator-prey models with delay in prey-specific growth rate, predator response function, and predator interaction time respectively. Subsequently, the impact of harvesting is analyzed in all the models. It is observed that varying delay could instigate instability in the system via Hopf-bifurcation. Taking harvesting as control can destroy such oscillatory behavior and bring the system to a stable dynamic. In this interplay between these two parameters, stability switching is observed, and such results could not be ascertained in the latter models. We have also inspected the system's behavior at maximum sustainable yield (MSY). If delay is small, harvesting at MSY could produce stable stock. Various numerical simulations are carried out to visualize our analytical findings.

Acknowledgments

The research work of Lakpa Thendup Bhutia is financially supported by Council of Scientific and Industrial Research (CSIR), India (File No. 08/0003(13400)/2022-EMR-I, dated: 4th March 2022) and the research work of Samir Biswas is financially supported by University Grants Commission, India (NTA Ref. No.: 201610175117, dated: 1st April 2021). The research of Tapan Kumar Kar is partially supported by the Council of Scientific and Industrial Research (CSIR), India (No. 25(0300)/19/EMR-II, dated: 16th May, 2019). Moreover, the authors are very much grateful to the anonymous reviewers, and the associate editor Jorge Duarte for their constructive comments and useful suggestions to improve the quality and presentation of the manuscript significantly.

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