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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

On the Dynamics of a Harvested Tri-trophic Food Chain Model with Alternative Food Source

Journal of Applied Nonlinear Dynamics 11(4) (2022) 845--861 | DOI:10.5890/JAND.2022.12.006

Lakshmi Narayan Guin$^{1}$, Sarmistha Pal$^{1}$, Muniyagounder Sambath$^{2}$

$^{1}$ Department of Mathematics, Visva-Bharati, Santiniketan-731 235, West Bengal, India

$^{2}$ Department of Mathematics, Periyar University, Salem-636 011, Tamil Nadu, India

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Abstract

A mathematical model addressing the phase transition scenario from stability to chaos in a three-species food chain model with alternative food source is presented in this research manuscript. The biological phenomenon of diverse solution trajectory formation has been uncovered here in terms of coupled nonlinear ordinary differential equations through positive initial conditions. The present paper is mainly focused on the existence and stability of coexistence equilibrium point as obtained by the system parameters and the interpretation of the result in terms of their possible ecological implications. The dynamics of the model reveal chaotic long-term behaviour over a broad range of parameters. The existence of a strange attractor and computation of the largest Lyapunov exponent also exhibit the presence of chaotic dynamics of our model. The final numerical simulations verify the correctness of our theoretical analysis.

Acknowledgments

The authors would like to express thanks to the eminent referees for their cooperative suggestions, which improved the quality of this research manuscript significantly. The first author gratefully acknowledges 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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