Singular homoclinic bifurcations in tritrophic food chains

DOI10.1016/S0025-5564(97)10001-3zbMath0927.92028WikidataQ52243022 ScholiaQ52243022MaRDI QIDQ1264478

O. De Feo, Sergio Rinaldi

Publication date: 16 December 1999

Published in: Mathematical Biosciences (Search for Journal in Brave)

zbMATH Keywords

homoclinic orbitsfood chain modelRosenzweig-MacArthur model

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Ecology (92D40)

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Uses Software

• HomCont

Cites Work

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• An application of the separation principle for detecting slow-fast limit cycles in a three-dimensional system
• Persistent unstable equilibria and closed orbits of a singularly perturbed equation
• Limit cycles in slow-fast forest-pest models
• Chaos in three species food chains
• Bifurcation structure of a three-species food chain model
• Remarks on food chain dynamics
• Non-standard analysis and singular perturbations of ordinary differential equations
• Low- and High-Frequency Oscillations in Three-Dimensional Food Chain Systems
• NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS
• Remarks on Competitive Coexistence
• Homoclinic bifurcations in slow-fast second order systems