Mathematical modelling of intraguild predation and its dynamics of resource harvesting

Document Type : Research Paper

Authors

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

Abstract

The contemporary theoretical inquest concerns itself with an updated mathematical model involving intraguild (IG) predation in which the IG predator acts as a generalist predator with the inclusion of harvesting in the resource population. Due attention is paid to the positivity and boundedness of the outcomes of the system under consideration. All the conceivable ecologically feasible equilibria are explored for their existence and stability under certain conditions. Special emphasis is put forward on the consequence of harvesting for the present model system. The occurrences of Hopf-bifurcation with respect to harvesting parameters involved in the harvesting effort of the model system are captured. The subsistence of the possible bionomic equilibria is, however, not ruled out from the present pursuit. The optimal harvesting policy is initiated and duly carried out with Pontryagin’s maximum principle. Numerical simulations are performed towards the end to comply with the objectives of the agreement of the numerical outcomes with their analytical counterparts and the applicability of the model is validated thereby.

Keywords

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Volume 13, Issue 2
July 2022
Pages 837-861
  • Receive Date: 27 January 2022
  • Revise Date: 30 March 2022
  • Accept Date: 12 April 2022