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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Dynamical Complexity in a Tritrophic Food Chain Model with Prey Harvesting

Discontinuity, Nonlinearity, and Complexity 10(4) (2021) 705--722 | DOI:10.5890/DNC.2021.12.010

Krishnendu Sarkar$^1$, Nijamuddin Ali$^2$, Lakshmi Narayan Guin$^1$

$^1$ Department of Mathematics, Visva-Bharati, Santiniketan, West Bengal, India, 731235

$^2$ Department of Mathematics, Vivekananda Mahavidyalaya, Purba Bardhaman, West Bengal, India, 713103

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Abstract

The present investigation deals with a tritrophic food web model with Holling-Tanner type II functional response to clarify the dynamical complexity of the eco-systems in the natural environment. The objective of this study is to explore the harvesting mechanism scenario in a three-dimensional interacting species system such as one prey and two specialist predators. Attention has been given to demonstrate the system characteristics near the biologically feasible equilibria. Specifically, stability, Hopf-Andronov bifurcation for the respective system parameters and dissipativeness has been performed in order to scrutinize the system behaviour. Lyapunov exponents are worked out numerically and an unstable scenario for significant parameters of the model system has been executed to characterize the complex dynamics. In addition to, we put forward a detailed numerical simulation to justify the chaotic dynamics of the present system. We conclude that chaotic dynamics can be executed by the prey harvesting parameters.

Acknowledgments

The present form of the paper owes much to the useful suggestions of the referees, whose careful study we are pleased to acknowledge. The first and third authors gratefully acknowledge the financial support in part from Special Assistance Programme (SAP-III) sponsored by the University Grants Commission (UGC), New Delhi, India (Grant No. F.510 / 3 / DRS-III / 2015 (SAP-I)).

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