Abstract
In this article, a one predator-one prey model incorporating Richards’ type growth in prey population, Hassell-Varley type functional response and Michaelis-Menten type prey harvesting is proposed and analyzed. Richards’ type growth with fear factor is incorporated in the proposed model to generalize the reduction effect of predator-induced fear on the rate of growth of the prey population. Positivity and boundedness of the system’s solutions are first established to ensure biological feasibility of the model. Existence and stability conditions of various types of equilibrium points associated with the model such as trivial equilibrium, axial (predator–free) equilibrium and coexistence equilibrium are obtained to analyze population dynamics. The effect of Richards’ intraspecific competition factor, Hassell-Varley constant, fear factor and harvesting constants on the dynamics of the coexistence equilibrium is then studied numerically using Python, highlighting the presence of Hopf-bifurcation. It is observed that decrease in predator–induced fear and net harvesting stabilizes the system; and the prevalence of social predatory behaviour among predators. Numerical simulations are presented to verify the results obtained analytically, and the biological relevance and significance of the model is discussed.
Recommended Citation
Bhattacharya, Aditya and Bhattacharyya, Anindita
(2026).
(SI16 No21) Dynamical Study of a Hassell-Varley Model with Nonlinear Harvesting and Fear Effect in Prey,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 21,
Iss.
3, Article 5.
Available at:
https://digitalcommons.pvamu.edu/aam/vol21/iss3/5