Global analysis of a predator-prey model with variable predator search rate

DOI10.1007/s00285-020-01504-yzbMath1448.34099arXiv1906.05960OpenAlexW3025985576WikidataQ94957390 ScholiaQ94957390MaRDI QIDQ782874

Jan Medlock, Patrick De Leenheer, Benjamin D. Dalziel, Enrique A. Thomann

Publication date: 29 July 2020

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.05960

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25) Stability of solutions to ordinary differential equations (34D20) Qualitative investigation and simulation of ordinary differential equation models (34C60) Global stability of solutions to ordinary differential equations (34D23) Asymptotic properties of solutions to ordinary differential equations (34D05) Dichotomy, trichotomy of solutions to ordinary differential equations (34D09)

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Cites Work

• A derivation of Holling's type I, II and III functional responses in predator-prey systems
• Stabilizing effects in spatial parasitoid-host and predator-prey models: a review
• Uniqueness of limit cycles in Gause-type models of predator-prey systems
• Global stability of predator-prey interactions
• Some results on global stability of a predator-prey system
• Graphical stability, enrichment, and pest control by a natural enemy
• The dynamics of two diffusively coupled predator--prey populations.
• Stability analysis of prey-predator system with Holling type functional response and prey refuge
• Sensitivity of the dynamics of the general Rosenzweig-Macarthur model to the mathematical form of the functional response: a bifurcation theory approach
• A mechanistic derivation of the DeAngelis-Beddington functional response
• Global stability of the predator-prey model with a sigmoid functional response
• The global stability of predator-prey system of Gause-type with Holling III functional response
• On the Uniqueness of a Limit Cycle for a Predator-Prey System
• Bifurcation Analysis of a Predator-Prey System Involving Group Defence
• Uniqueness of a Limit Cycle for a Predator-Prey System
• On a predator-prey system of Holling type
• The Theory of the Chemostat