A mathematical analysis of harvesting in tri-trophic food chain with complex dynamics

Authors

  • Krishna pada Das Mahadevananda Mahavidyalaya Department Of Mathematics Monirampore P.O.-Barrackpore Kol-120
  • Abhishek Sarkar Department of Mathematics, Mahadevananda Mahavidyalaya,\\Barrackpore,kol-120, Indian
  • Seema Sarkar (Mondal $Department of Mathematic, NIT Durgapur, India
  • Partha Karmakar $WBES deputy secretary west bengal board of primary education ,\\ Saltlake City, Kol-700091
  • Gaurishankar Paliwal $Department of Mathematics, JECRC university, Jaipur, India\\
  • Rakesh Kumar $Department of Mathematics, SBSSU, Ferozpur, punjab, India

Abstract

The present paper explores a tri-trophic food chain model with three species and harvesting in prey with complex dynamics. Here we
 discuss the HP model and Holling type-II function. We nd the Extinction criteria of species and boundedness . We also derived the co dition of existence and stability of equilibrium points. To investigate  the local stability and Hopf-bifurcation. Also discuss the Permanence and Impermanence of the system for future time. In the complex dynamical system we observed stable focus, limit cycle, period doubling and chaotic dynamics of the system. We observe that chaotic oscillations in a tri-trophic food chain model is common and control of such oscillation is utmost important from ecological as well as economical  viewpoint.

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Published

2024-08-29

Issue

Vol. 31 No. 3 (2024): Nonlinear Studies (NS)

Section

Articles

License

Copyright (c) 2024 Krishna pada Das, Abhishek Sarkar, Seema Sarkar (Mondal, Partha Karmakar, Gaurishankar Paliwal, Rakesh Kumar

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

A mathematical analysis of harvesting in tri-trophic food chain with complex dynamics. (2024). Nonlinear Studies, 31(3), 857-873. https://nonlinearstudies.com/index.php/nonlinear/article/view/3183