Several bifurcation mechanisms for limit cycles in a predator-prey system

DOI10.1007/s12346-021-00501-wzbMath1477.34075OpenAlexW3180831488WikidataQ115601489 ScholiaQ115601489MaRDI QIDQ1981903

André Zegeling, Robert E. Kooij

Publication date: 7 September 2021

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-021-00501-w

zbMATH Keywords

singular perturbationcenterlimit cyclefunctional responseHollinggeneralized Gause model

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) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Qualitative investigation and simulation of ordinary differential equation models (34C60) Singular perturbations for ordinary differential equations (34E15)

Related Items (2)

Qualitative and bifurcation analysis in a Leslie-Gower model with Allee effect ⋮ Perturbation of a piecewise regular-singular Liénard system

Cites Work

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• Canard solutions at non-generic turning points
• Canard cycles in the presence of slow dynamics with singularities
• Uniqueness of limit cycles in polynomial systems with algebraic invariants
• Canard cycles and center manifolds
• Co-existence of a Period Annulus and a Limit Cycle in a Class of Predator–Prey Models with Group Defense
• Multiple canard cycles in generalized Liénard equations

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