Trajectories of Cannibalism Interaction with Holling Type II and Monod–Haldane Functional Responses

Rian Ade Pratama; Dessy Rizki Suryani; Maria F. V. Ruslau; Etriana Meirista

doi:10.31764/jtam.v10i2.36659

Trajectories of Cannibalism Interaction with Holling Type II and Monod–Haldane Functional Responses

Rian Ade Pratama, Dessy Rizki Suryani, Maria F. V. Ruslau, Etriana Meirista

Abstract

The stability and equilibrium behavior of predator–prey systems involving cannibalistic interactions is crucial for explaining the long-term sustainability of ecological communities. This study aims to analyze the dynamics of a modified predator–prey model by incorporating cannibalism in predators as a self-regulating mechanism influencing population control. This study is a literature-based research, and the instruments employed are non-physical in nature, including a mathematical model, mathematical analysis tools, and numerical computation frameworks. The research methodology employs literature review and analysis of a model formulated as a system of nonlinear differential equations. This system describes the population dynamics of two prey species and one predator species exhibiting cannibalistic tendencies. Analytical and numerical approaches are utilized to determine equilibrium points, evaluate local stability, and assess the effects of density-dependent mortality and cannibalistic behavior on ecosystem balance. The results show that the proposed predator–prey model admits one trivial equilibrium, five semi-trivial equilibrium, and one coexistence equilibrium. The coexistence equilibrium is locally asymptotically stable and satisfies the Routh–Hurwitz stability criterion. Simulation numeric the cannibalism parameter and density-dependent mortality rates play a significant role in stabilizing the predator population dynamics. When the mortality coefficient increases, the predator population decreases toward a lower equilibrium point, while the prey population slightly increases due to reduced predation pressure. Eigenvalue analysis reinforces these findings by confirming the system's compliance with the Routh–Hurwitz stability conditions. Ecological implications, these findings suggest that cannibalistic behavior in predators acts as a natural feedback mechanism to regulate population density, enhance ecosystem stability, and support the long-term sustainability of predator–prey interactions. The cannibalistic character of the predator species does not necessarily lead to species extinction, but can instead facilitate a sustainable and balanced coexistence within the ecosystem.

Keywords

Cannibalisme; Holling type II; Monod-Haldane; Nonlinear differential equations; Predator-prey dynamics.

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DOI: https://doi.org/10.31764/jtam.v10i2.36659