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Summary

Generalist predators using Holling III functional response drive complex ecological dynamics. Their prey-switching behavior in predator-prey models leads to rich bifurcations and population coexistence.

Keywords:
Generalist predationGlobal stabilityHolling III functional responseHopf bifurcationNilpotent bifurcationPredator-prey model

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Theoretical Ecology

Background:

  • Generalist predators exhibit prey-switching behavior, crucial for population dynamics.
  • The Holling III functional response models predator feeding behavior effectively.
  • Leslie-type predator-prey models are foundational in ecological dynamics.

Purpose of the Study:

  • To analyze a Leslie-type predator-prey model with generalist predation and Holling III functional response.
  • To investigate the bifurcation phenomena and stability of the model.
  • To understand the role of prey-switching in ecological systems.

Main Methods:

  • Establishing the existence of nilpotent cusps/foci and weak foci.
  • Analyzing bifurcations, including nilpotent cusp/focus (codimension 3) and Hopf (codimension 2).
  • Deriving conditions for global asymptotic stability of the positive equilibrium.

Main Results:

  • The Holling III functional response promotes population coexistence.
  • The model exhibits rich bifurcation phenomena, including tristability and multiple limit cycles.
  • Prey-switching behavior significantly influences system dynamics and bifurcation thresholds.

Conclusions:

  • Generalist predators and the Holling III response create complex ecological dynamics.
  • Prey-switching is a key factor in regulating population stability and emergent behaviors.
  • The study provides insights into the intricate dynamics of predator-prey systems.