Stability and Turing Patterns of a Predator-prey Model with Holling Type II Functional Response and Allee Effect in Predator

Chen, Lu; Feng, Yang; Song, Yongli

doi:10.1007/s10255-023-1084-1

Acta Math. Appl. Sin. Engl. Ser.

2023

DOI: 10.1007/s10255-023-1084-1

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Stability and Turing Patterns of a Predator-prey Model with Holling Type II Functional Response and Allee Effect in Predator

Lu Chen

Yang Feng

Yongli Song

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Cited by 2 publications

References 41 publications

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Stability and Bifurcation of a Gordon–Schaefer Model with Additive Allee Effect

Liao,

Song,

Xia

2024

Int. J. Bifurcation Chaos

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The rarity of species increases its market price, consequently leading to the overexploitation of the species and even the extinction of the species. We study how the harvest intensity and the additive Allee effect impact on the Gordon–Schaefer model. In addition, by Sotomayor’s theorem and Poincaré–Andronov theorem, we prove the existence of Hopf bifurcation, saddle-node bifurcation and transcritical bifurcation, respectively. Finally, we illustrate our results by numerical simulations. We find that both the cost per unit of harvest and the additive Allee effect have a significant impact on human exploitation of the population. As the additive Allee effect reduces to the weak Allee effect, the lower harvest cost encourages humans to increase the exploitation of species. This threshold is a switch that controls the strong Allee effect. If it exceeds its threshold, then the motivation of humans to exploit the species increases.

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Stability and Bifurcation of a Gordon–Schaefer Model with Additive Allee Effect

Liao,

Song,

Xia

2024

Int. J. Bifurcation Chaos

View full text Add to dashboard Cite

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Stability analysis of a Filippov Gause predator-prey model with or without hunting cooperation among predators with respect to prey density

Cortés-García

2025

DCDS

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This paper investigates two new Filippov-Gause predator-prey models that show the transition between individual and cooperative hunting dynamics among predators with respect to the critical prey population size. By using Filippov systems, this research offers a more realistic and complete representation of the nonlinear dynamics and discontinuities inherent in this complex ecological system so that the proposed models provide a more complete view of predator-prey interactions in different realistic environmental contexts. For the case where predators only cooperate in hunting when the prey population size is larger than its critical value, we could have at least one asymptotically stable limit cycle around a single positive inner equilibrium, or two limit cycles around the pseudo-stable equilibrium. However, in the case where predators only cooperate in hunting when the prey population size is less than its critical value, we could have one limit cycle around two inner equilibria and one pseudo-equilibrium that is unstable. In general, as the two proposed models differ in the presence of a sliding or escaping segment, the overall dynamics and bifurcation diagrams of both models change significantly.

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Stability and Turing Patterns of a Predator-prey Model with Holling Type II Functional Response and Allee Effect in Predator

Cited by 2 publications

References 41 publications

Stability and Bifurcation of a Gordon–Schaefer Model with Additive Allee Effect

Stability and Bifurcation of a Gordon–Schaefer Model with Additive Allee Effect

Stability analysis of a Filippov Gause predator-prey model with or without hunting cooperation among predators with respect to prey density

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