Dynamical analysis of a three-species model with logistic growth and holling type II functional responses in a Predator-Prey system

Abstract

This paper presents a modified three-species intraguild predator-prey model describing the interactions among lions (), leopards (), and hares () in an ecosystem. The linear model proposed by Kwaghkor et al. (2024) is modified by incorporating logistic growth terms for all populations and replacing the Type I functional responses with saturating Holling Type II functional responses. The resulting system of three nonlinear ordinary differential equations is analyzed for positivity, boundedness, existence of equilibria, and local asymptotic stability. Using the Jacobian matrix and the Routh–Hurwitz criterion, explicit stability conditions are derived for the trivial, single-species, and interior equilibria. Numerical simulations were performed with parameter sets adapted from the work of Kwaghkor et al. (2024). The modified model eliminates the unrealistic persistent oscillations observed in the work of Kwaghkor et al. (2024) linear system and demonstrates convergence to either a stable interior coexistence equilibrium depending on relative predation strengths and carrying capacities. The results confirm that the incorporation of density dependence and saturating functional responses produce qualitative realistic and mathematically robust dynamics. This enhanced model provides a more reliable framework for studying intraguild prey-predation in savanna ecosystems and offers practical insights for wildlife conservation.