The Rosenzweig-MacArthur system via reduction of an individual based model

DOI10.1007/s00285-018-1278-yzbMath1410.92101OpenAlexW2885715008WikidataQ90863958 ScholiaQ90863958MaRDI QIDQ1738031

Niclas Kruff, Christian Lax, Volkmar Liebscher, Sebastian Walcher

Publication date: 29 March 2019

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

Full work available at URL: https://doi.org/10.1007/s00285-018-1278-y

zbMATH Keywords

functional responsepredator-prey modelsingular perturbation theoryHolling disk functionTikhonov-Fenichel parameters

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Population dynamics (general) (92D25) Ecology (92D40)

Related Items

Quasi-Steady-State and Singular Perturbation Reduction for Reaction Networks with Noninteracting Species, Coordinate-independent criteria for Hopf bifurcations, Dynamical analysis of conformable fractional-order Rosenzweig-MacArthur prey-predator system

Uses Software

• SINGULAR

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A constructive approach to quasi-steady state reductions
• A derivation of Holling's type I, II and III functional responses in predator-prey systems
• Predator-prey models in heterogeneous environment: emergence of functional response
• Holling's hungry mantid model for the invertebrate functional response considered as a Markov process. III. Stable satiation distribution
• Geometric singular perturbation theory for ordinary differential equations
• Singular perturbation methods for ordinary differential equations
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Effects of spatial grouping on the functional response of predators
• On transformations into normal form
• On the Poincaré problem
• Mathematical biology. Vol. 1: An introduction.
• Type II functional response for continuous, physiologically structured models
• Classical quasi-steady state reduction -- a mathematical characterization
• A mechanistic derivation of the DeAngelis-Beddington functional response
• Holling's hungry mantid model for the invertebrate functional response considered as a Markov process. I: The full model and some of its limits
• Holling's hungry mantid model for the invertebrate functional response considered as a Markov process. II: Negligible handling time
• Group defence and the predator's functional response
• Coordinate-independent criteria for Hopf bifurcations
• Geometric singular perturbation theory in biological practice
• Determining ``small parameters for quasi-steady state
• The DeAngelis-Beddington functional response and the evolution of timidity of the prey
• Paradox of enrichment and system order reduction: bacteriophages dynamics as case study
• The Quasi-Steady-State Assumption: A Case Study in Perturbation
• The Theory of the Chemostat