2020/09/06 by Claudio Arancibia–Ibarra, Arancibia-Ibarra, Claudio, Flores, Jos/'e
Biochemistry, Genetics and Molecular Biology · Medicine · Social Sciences · #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.2009.04246
openalex publication_date 2020/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A predator-prey model with functional response Holling type II, Allee effect in the prey and a generalist predator is considered. It is shown that the model with strong Allee effect has at most two positive equilibrium point in the first quadrant, one is always a saddle point and the other exhibits multi-stability phenomenon since the equilibrium point can be stable or unstable. While the model with weak Allee effect has at most three positive equilibrium point in the first quadrant, one is always a saddle point and the other two can be stable or unstable node. In addition, when the parameters vary in a small neighbourhood of system parameters the model undergoes to different bifurcations, such as saddle-node, Hopf and Bogadonov-Takens bifurcations. Moreover, numerical simulation is used to illustrate the impact in the stability of positive equilibrium point(s) by adding an Allee effect and an alternative food source for predators.