Additive Allee effect on prey in the dynamics of a Gause predator–prey model with constant or proportional refuge on prey at low or high densities

García, Christian Cortés; Cuenca, Jasmidt Vera

doi:10.1016/j.cnsns.2023.107427

Communications in Nonlinear Science and Numerical Simulation

2023

DOI: 10.1016/j.cnsns.2023.107427

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Additive Allee effect on prey in the dynamics of a Gause predator–prey model with constant or proportional refuge on prey at low or high densities

Christian Cortés García

Jasmidt Vera Cuenca

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Cited by 4 publications

References 42 publications

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Population dynamics in a Leslie–Gower predator–prey model with predator harvesting at high densities

Cortés García

2024

Math Methods in App Sciences

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In this paper, we propose a Leslie–Gower predator–prey model in which the predator can only be captured when its population size exceeds a critical value; the mean growth rate of the prey in the absence of the predator is subject to a semi‐saturation rate that affects its birth curve, and the interaction between the two species is defined by a Holling II predation functional with alternative food for the predator. Since the proposed model is equivalent to a Filippov system, its mathematical analysis leads to a local study of the equilibria in each vector field corresponding to the proposed model, in addition to the study of the stability of its pseudo‐equilibria located on the curve separating the two vector fields. In particular, the model could have between one and three pseudo‐equilibria and at least one limit cycle surrounding one or two inner equilibria, locally unstable points.

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Population dynamics in a Leslie–Gower predator–prey model with predator harvesting at high densities

Cortés García

2024

Math Methods in App Sciences

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Population dynamics in a Leslie-Gower predator-prey model with proportional prey refuge at low densities

Cortés-García

2025

Journal of Mathematical Analysis and Applications

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Dynamical Analysis of a Predator–Prey Model with Additive Allee Effect and Migration

Huang,

Chen,

Xia

et al. 2023

Int. J. Bifurcation Chaos

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In this paper, a predator–prey model in which the prey has the additive Allee effect and the predator has artificially controlled migration is proposed. When the system introduces additive Allee effect and artificially controlled migration, more complicated dynamical behavior is obtained. The system can undergo saddle-node bifurcation, transcritical bifurcation, pitchfork bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation. Two limit cycles are found and discussed. The influence of the additive Allee effect and artificially controlled migration on the dynamics of the system is also presented. In detail, when the Allee effect is large, the prey will become extinct. When the artificially controlled migration rate is larger, the intensity of the prey (pest) will be smaller and the intensity of the predator will be larger. This indicates that artificially controlled migration can be effectively used to control the pest.

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Additive Allee effect on prey in the dynamics of a Gause predator–prey model with constant or proportional refuge on prey at low or high densities

Cited by 4 publications

References 42 publications

Population dynamics in a Leslie–Gower predator–prey model with predator harvesting at high densities

Population dynamics in a Leslie–Gower predator–prey model with predator harvesting at high densities

Population dynamics in a Leslie-Gower predator-prey model with proportional prey refuge at low densities

Dynamical Analysis of a Predator–Prey Model with Additive Allee Effect and Migration

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