The Dynamics of Delayed Population Systems with Age-selective Harvesting: Interactions Between Stability, Bifurcations, and Bio-economic Efficiency

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics, Central University of Odisha-763004, Koraput, Odisha, India.

Abstract

This study examines the dynamic behaviour of salmon populations using the Leslie-Gower model, incorporating a Beddington-DeAngelis type functional response and non-linear harvesting targeting prey beyond a certain age. The analysis addresses several key aspects, including optimal harvesting strategies, bionomics equilibrium, Maximum Sustainable Yield (MSY), and qualitative dynamics of the system. Special attention is given to the asymptotic stability and delay-dependent nature of the internal equilibrium. A Hopf bifurcation is identified in relation to the maturation delay. To determine an optimal harvesting trajectory after reaching the MSY, Pontryagin’s maximum principle is applied, with the existence of the bionomic equilibrium also taken into account. Numerical simulations are employed to further elucidate the system's behaviour and gain deeper insights into its dynamics.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 12 July 2026

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History

  • Receive Date: 14 August 2025
  • Revise Date: 09 July 2026
  • Accept Date: 11 July 2026

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