Analytical search for bifurcation surfaces in parameter space

DOI10.1016/j.physd.2004.03.019zbMath1056.37070OpenAlexW2128030575MaRDI QIDQ1886991

Thilo Gross, Ulrike Feudel

Publication date: 23 November 2004

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2004.03.019

zbMATH Keywords

Hopf bifurcationBifurcation detectionHigher codimension bifurcations

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Dynamics induced by flows and semiflows (37C10) Two-body problems (70F05) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Dynamical systems in classical and celestial mechanics (37N05) Genetics and population dynamics (92D99)

Related Items (10)

Detection and computation of high codimension bifurcations in diffuse predator-prey systems ⋮ Evolutionary distributions: producer–consumer pattern formation ⋮ COMPUTATION AND VISUALIZATION OF BIFURCATION SURFACES ⋮ Enrichment and foodchain stability: the impact of different forms of predator-prey interaction ⋮ Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations ⋮ A stage-structured food chain model with stage dependent predation: existence of codimension one and codimension two bifurcations ⋮ Bifurcation analysis of an ecological food-chain model with switching predator ⋮ Control algorithm for creation of Hopf bifurcations in continuous-time systems of arbitrary dimension ⋮ Revealing instabilities in a generalized triadic supply network: A bifurcation analysis ⋮ Stability of generalized ecological-network models

Uses Software

• CANDYS/QA
• DSTool
• Dynamics

Cites Work

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• NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (I): BIFURCATION IN FINITE DIMENSIONS
• Computing Hopf Bifurcations. II: Three Examples From Neurophysiology
• Computation of Hopf Bifurcation with Bordered Matrices
• A new approach to the perturbation theory of invariant surfaces
• Elements of applied bifurcation theory

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