Dynamical Behavior in Prey-Predator Model with Mutualistic Protection for Prey

Laras Kinanti Putri, Dian Savitri, Abadi Abadi

Abstract


This article reconstructs the model of predator-prey mutualistic protection based on a journal written by Revilla and Krivan (2022). The predator-prey model considers mutualistic protection for the prey. The model focuses on the analysis of equilibrium points and combines an adaptive model to study the influence of both models on predator-prey dynamics. This research continues the stability analysis and numerical simulations of the predator-prey model with mutualistic protection to examine the impact of mutualistic protection on prey dynamics in the model. The research process begins with a literature review, reconstructing the predator-prey model, determining equilibrium points, analyzing stability at the equilibrium points, conducting numerical simulations including bifurcation diagrams and phase portraits of the model solutions, and drawing conclusions. The analysis yields three equilibrium points: the unstable co-extinction of both populations, predator extinction, and the conditionally stable coexistence of both populations. Based on the analysis results, there are changes in the system solutions, with the originally stable E3 becoming unstable. There is also a change in E2 from being unstable to stable. Through numerical continuation with variations in the parameter representing the mutualistic protector’s preference for prey resources (u), a transcritical bifurcation (Branch Point) is obtained at u = 0.888889. The simulation results demonstrate that (u) can influence the stability of predator and prey populations.

Keywords


Protection Mutualism; Stability; Numerical Simulation

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References


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DOI: https://doi.org/10.37905/jjbm.v4i2.21541

Copyright (c) 2023 Laras Kinanti Putri, Dian Savitri, Abadi Abadi

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