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Bifurcation analysis of a predator-prey model with predator intraspecific interactions and ratio-dependent functional response

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  • Arancibia-Ibarra, Claudio
  • Aguirre, Pablo
  • Flores, José
  • van Heijster, Peter

Abstract

We study the Bazykin predator-prey model with predator intraspecific interactions and ratio-dependent functional response and show the existence and stability of two interior equilibrium points. We prove that the model displays a wide range of different bifurcations, such as saddle-node bifurcations, Hopf bifurcations, homoclinic bifurcations and Bogdanov-Takens bifurcations. We use numerical simulations to further illustrate the impact changing the predator per capita consumption rate has on the basin of attraction of the stable equilibrium points, as well as the impact of changing the efficiency with which predators convert consumed prey into new predators.

Suggested Citation

  • Arancibia-Ibarra, Claudio & Aguirre, Pablo & Flores, José & van Heijster, Peter, 2021. "Bifurcation analysis of a predator-prey model with predator intraspecific interactions and ratio-dependent functional response," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    • Handle: RePEc:eee:apmaco:v:402:y:2021:i:c:s0096300321002009
    DOI: 10.1016/j.amc.2021.126152
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    References listed on IDEAS

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    1. Shi, Hong-Bo & Li, Yan, 2015. "Global asymptotic stability of a diffusive predator–prey model with ratio-dependent functional response," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 71-77.
    2. Bartumeus, Fede & Alonso, David & Catalan, Jordi, 2001. "Self-organized spatial structures in a ratio-dependent predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(1), pages 53-57.
    3. Liu, Rongsong & DeAngelis, Donald L. & Bryant, John P., 2014. "Ratio-dependent functional response emerges from optimal foraging on a complex landscape," Ecological Modelling, Elsevier, vol. 292(C), pages 45-50.
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    Cited by:

    1. Pranali Roy Chowdhury & Sergei Petrovskii & Malay Banerjee, 2022. "Effect of Slow–Fast Time Scale on Transient Dynamics in a Realistic Prey-Predator System," Mathematics, MDPI, vol. 10(5), pages 1-12, February.
    2. Tian, Yuan & Li, Huanmeng & Sun, Kaibiao, 2024. "Complex dynamics of a fishery model: Impact of the triple effects of fear, cooperative hunting and intermittent harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 31-48.

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