A note on the calculation of paths of Hopf bifurcations

DOI10.1016/0377-0427(89)90151-9zbMath0684.65057OpenAlexW2042905181MaRDI QIDQ1825601

A. D. Jepson, K. Andrew Cliffe, Alastair Spence

Publication date: 1989

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(89)90151-9

zbMATH Keywords

Banach spacecomplex eigenvaluespitchforkextended systemHopf bifurcation pointsapproximation of branchesBogdanov-Takens bifurcation pointsymmetry-breaking bifurcation pointtwo-parameter nonlinear system

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Numerical solutions to equations with nonlinear operators (65J15) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17) Local and nonlocal bifurcation theory for dynamical systems (37G99)

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Hopf bifurcation near a double singular point, The numerical computation of symmetry-breaking Takens-Bogdanov points, Computation of Hopf branches bifurcating from a class of Hopf/steady-state points, Analysis of Takens-Bogdanov bifurcation by characteristic functions, On nondegeneracy of hopf bifurcation points emanating from a takens-bogdanov point, Asymptotic analysis of perturbed Takens-Bogdanov points, A new approach for the computation of Hopf bifurcation points, Interaction between fold and Hopf curves leads to new bifurcation phenomena, Nondegeneracy of Hopf points emanating from a \(Z_ 2\)-symmetry-breaking Takens-Bogdanov point, A note on the calculation of paths of Hopf bifurcations, THE CALCULATION OF THE HOPF/HOPF MODE INTERACTION POINT IN PROBLEMS WITH Z₂-SYMMETRY, Computing a closest bifurcation instability in multidimensional parameter space, A numerical approach to hopf bifurcation points, Hopf bifurcation near a double singular point with \(\mathbb{Z}_{2}\)-symmetry and \(X_{0}\)-breaking

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• A note on the calculation of paths of Hopf bifurcations
• The Computation of Symmetry-Breaking Bifurcation Points
• The Calculation of Hopf Points by a Direct Method
• Numerical Determination of an Emanating Branch of Hopf Bifurcation Points in a Two-Parameter Problem
• The Calculation of Turning Points of Nonlinear Equations