Sensitivity of the dynamics of the general Rosenzweig-Macarthur model to the mathematical form of the functional response: a bifurcation theory approach

DOI10.1007/s00285-017-1201-yzbMath1390.92123OpenAlexW2782415615WikidataQ47196139 ScholiaQ47196139MaRDI QIDQ1750656

Gunog Seo, Gail S. K. Wolkowicz

Publication date: 22 May 2018

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

Full work available at URL: https://doi.org/10.1007/s00285-017-1201-y

zbMATH Keywords

functional responsetrigonometricHolling type IIIvlevRosenzweig-MacArthur predator-prey modelsaddle-node of limits cycles bifurcation

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25)

Related Items (16)

Global Stability of a Predator-Prey Model with Ivlev-Type Functional Response ⋮ A Predator-Prey model in the chemostat with Holling Type II response function ⋮ Food sharing and time budgeting in predator-prey interaction ⋮ Dynamics of the discrete-time Rosenzweig-MacArthur predator-prey system in the closed positively invariant set ⋮ No sensitivity to functional forms in the Rosenzweig-MacArthur model with strong environmental stochasticity ⋮ A nonautonomous model for the interaction between a size-structured consumer and an unstructured resource ⋮ Steady‐state bifurcation and Hopf bifurcation in a cross‐diffusion prey–predator system with Ivlev functional response ⋮ The Rosenzweig-MacArthur graphical criterion for a predator-prey model with variable mortality rate ⋮ Number and Stability of Relaxation Oscillations for Predator-Prey Systems with Small Death Rates ⋮ Pest control by generalist parasitoids: a bifurcation theory approach ⋮ Predator - prey/host - parasite: a fragile ecoepidemic system under homogeneous infection incidence ⋮ Global stability of the predator-prey model with a sigmoid functional response ⋮ Competitive exclusion and coexistence in an intraguild predation model with Beddington-DeAngelis functional response ⋮ Bifurcation analysis of the predator-prey model with the Allee effect in the predator ⋮ Global analysis of a predator-prey model with variable predator search rate ⋮ Bifurcation and overexploitation in Rosenzweig-MacArthur model

Uses Software

• Matlab
• XPPAUT

Cites Work

• Unnamed Item
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• Mathematical biology. Vol. 1: An introduction.
• A predator-prey model with Ivlev's functional response
• A comparison of two predator-prey models with Holling's type I functional response
• Existence of multiple limit cycles in a predator-prey model with \(\arctan(ax)\) as functional response
• Simulating, Analyzing, and Animating Dynamical Systems
• THE EXTENT OF ASYMPTOTIC STABILITY
• 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
• Competing Predators
• Elements of Mathematical Ecology
• Elements of applied bifurcation theory

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