Stability analysis of a delay logistic growth model with nonlinear harvesting

Martin Anokye, Sampson Z. Nkangbi, Agnes A. Konadu, Albert L. Sackitey, John A. Mensah, Luca Guerrini and Massimiliano Ferrara ()
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Martin Anokye: University of Cape Coast
Sampson Z. Nkangbi: University of Cape Coast
Agnes A. Konadu: University of Cape Coast
Albert L. Sackitey: University of Cape Coast
John A. Mensah: Sunyani Technical University
Luca Guerrini: Polytechnic University of Marche
Massimiliano Ferrara: Mediterranea University of Reggio Calabria

Quality & Quantity: International Journal of Methodology, 2025, vol. 59, issue 6, No 14, 5253-5268

Abstract: Abstract This research compares the population dynamics of a delayed logistic model, which incorporates a nonlinear harvesting function and accounts for the species’ developmental period, with a traditional model lacking both time delay and developmental period considerations. The findings demonstrate that the traditional model reaches equilibrium faster across all studied cases, while the delayed model exhibits a response lag to changes in independent variables. However, the delayed logistic model with nonlinear harvesting reveals ecological characteristics, such as a critical bifurcation threshold and stability variations, that are absent in the traditional model. Stability analysis further indicates that shorter time delays correlate with faster population growth, and longer delays with slower growth. Overall, the study suggests that the delayed logistic model is less conducive to unrestricted population increases, particularly compared to logistic models with constant and linear harvesting functions. Nevertheless, due to the nonlinear nature of most ecological systems, this model is recommended for population modeling as it can be adapted to reflect both new and existing models, enhancing its applicability for real-world simulations.

Keywords: Discrete delay; Nonlinear harvesting; Stability; Hopf bifurcation (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11135-025-02203-w

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