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Does mutual interference stabilize prey-predator model with Bazykin-Crowley-Martin trophic function?

Yuri Tyutyunov1, Deeptajyoti Sen2, Malay Banerjee3

  • 1Southern Scientific Centre of the Russian Academy of Sciences, 41 Chekhov St., Rostov-on-Don, 344006, Russia.

Mathematical Biosciences
|April 18, 2024
PubMed
Summary
This summary is machine-generated.

Predator interference, modeled using the Bazykin-Crowley-Martin (BCM) function, impacts prey-predator dynamics. Moderate interference stabilizes the ecosystem, while extreme levels risk predator extinction.

Keywords:
Bifurcation analysisDestabilizing effectExtinction riskFunctional responseMutual interference of predatorsStabilizing effect

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Theoretical Ecology

Background:

  • Predator-prey models are crucial for understanding ecosystem stability.
  • The Allee effect and predator interference significantly influence population dynamics.
  • The Bazykin-Crowley-Martin (BCM) trophic function models mutual interference among predators.

Purpose of the Study:

  • To analyze the impact of predator mutual interference on prey-predator system dynamics.
  • To investigate the stabilizing or destabilizing effects of predator interference using the BCM trophic function.
  • To derive analytical conditions for various bifurcations in the model.

Main Methods:

  • Developed a system of ordinary differential equations incorporating the Allee effect and BCM trophic function.
  • Performed bifurcation analysis to identify critical parameter values and transitions in system behavior.
  • Conducted numerical simulations to validate analytical findings and visualize dynamics.

Main Results:

  • Identified conditions for saddle-node, Hopf, cusp, and Bogdanov-Takens bifurcations.
  • Quantified the influence of predator interference strength, Allee effect, and predation efficiency on bifurcations.
  • Observed that both low and very high predator interference increase extinction risk.

Conclusions:

  • Moderate predator interference promotes stability and resilience in prey-predator systems.
  • The BCM trophic function reveals a non-monotonic relationship between interference and system stability.
  • Findings align with other predator-dependent models, highlighting the critical role of interference levels.