Dynamics in two competing predators-one prey system with two types of Holling and fear effect

Adin Lazuardy Firdiansyah, Nurhidayati Nurhidayati

Abstract


In this article, it is formulated a predator-prey model of two predators consuming a single limited prey resource. On the other hand, two predators have to compete with each other for survival. The predation function for two predators is assumed to be different where one predator uses Holling type I while the other uses Holling type II. It is also assumed that the fear effect is considered in this model as indirect influence evoked by both predators. Non-negativity and boundedness is written to show the biological justification of the model. Here, it is found that the model has five equilibrium points existed under certain condition. We also perform the local stability analysis on the equilibrium points with three equilibrium points are stable under certain conditions and two equilibrium points are unstable. Hopf bifurcation is obtained by choosing the consumption rate of the second predator as the bifurcation parameter. In the last part, several numerical solutions are given to support the analysis results.

Keywords


Holling Functional Response; Hopf Bifurcation; Local Stability; Predator-Prey Model

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DOI: https://doi.org/10.34312/jjbm.v2i2.11264

Copyright (c) 2021 Adin Lazuardy Firdiansyah, Nurhidayati

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