Multiple bifurcation in a predator–prey system with nonmonotonic predator response

DOI10.1017/S0308210500032169zbMath0763.92011WikidataQ115562895 ScholiaQ115562895MaRDI QIDQ4009963

Franz Rothe, Douglas S. Shafer

Publication date: 27 September 1992

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

stable equilibriummultiple bifurcationscoordinate transformationspredator-prey systemgeneralized Gause modelenrichment paradoxVolterra-Lotka systembifurcation of cycles from infinitycodimension- two singularity of cusp typecoexistence of stable oscillationsgroup-defenceprey logistic growthsemi-stable bifurcation of cyclesthree-parameter family of quartic polynomial systems of equations

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Ecology (92D40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (14)

Geometric criteria for the non-existence of cycles in predator-prey systems with group defense ⋮ Global analysis in Bazykin's model with Holling II functional response and predator competition ⋮ Global Stability and Canard Explosions of the Predator-Prey Model with the Sigmoid Functional Response ⋮ Singular perturbations of the Holling I predator-prey system with a focus ⋮ High codimension bifurcations of a predator-prey system with generalized Holling type III functional response and Allee effects ⋮ Modelling the dynamics in a predator-prey system with Allee effects and anti-predator behavior ⋮ Predator-prey models with non-analytical functional response ⋮ Bifurcation analysis of a predator-prey model with anti-predator behaviour ⋮ Co-existence of a Period Annulus and a Limit Cycle in a Class of Predator–Prey Models with Group Defense ⋮ Higher Codimension Bifurcation Analysis of Predator–Prey Systems with Nonmonotonic Functional Responses ⋮ CODIMENSION TWO BIFURCATIONS IN A PREDATOR–PREY SYSTEM WITH GROUP DEFENSE ⋮ Monotonic and nonmonotonic immune responses in viral infection systems ⋮ Dynamics analysis of a predator-prey model with nonmonotonic functional response and impulsive control ⋮ Slow-Fast Dynamics and Its Application to a Biological Model

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Abelian integrals and bifurcation theory
• Predator-prey systems with group defence: The paradox of enrichment revisited
• A note on: Abelian integrals and bifurcation theory
• Bifurcation formulae derived from center manifold theory
• Singularities of vector fields on the plane
• Bifurcations and trajectories joining critical points
• Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3
• Bifurcation Analysis of a Predator-Prey System Involving Group Defence
• Generic Properties of Polynomial Vector Fields at Infinity

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