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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

Response of Prey-Predator-Scavenger Interactions with the Inclusion of Prey Harvesting

Journal of Applied Nonlinear Dynamics 13(2) (2024) 279--306 | DOI:10.5890/JAND.2024.06.008

Lakshmi Narayan Guin, Gourav Mandal, Pallab Pal, Santabrata Chakravarty

Department of Mathematics, Visva-Bharati, Santiniketan-731 235, West Bengal, India

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Abstract

The proposed analytical investigation deals with the interactions between prey, predator, and scavenger population in the event of prey harvesting through the use of an updated mathematical model. It includes the usage of the modified Previte and Hoffman tri-trophic food web model along with its issues governing the system of nonlinear differential equations. The prey population is assumed to follow a logistic growth with predation from both the predator and the scavenger population. The intervention of prey harvesting is another inclusion of the concerned study for the purpose of having a complete understanding of the influence of both the predator and scavenger species. The present attempt intends to explore the mechanism of harvesting scenario in a three-dimensional system of interacting species, namely one prey and two specialist predators. At the onset, the proposed model is sought for dimension-free so as to reduce the number of model parameters of the system successfully. The existence of feasible equilibria, together with their topological classification regarding coexistence positive equilibrium points of the system is thoroughly examined.~The stability analysis is carried out for all the feasible equilibria of the system in order to understand the dynamics of the interacting species. The sensitivity analysis of the model system is also performed numerically so as to estimate the harvesting rate culpable for balancing biomass. One may perceive that so long as the harvesting rate is uncontrolled, that is, beyond the threshold value, both the predator and scavenger species become extinct together with the prey population.

Acknowledgments

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