An algorithm for the computation of Hopf bifurcation points in comparison with other methods

DOI10.1016/0377-0427(85)90045-7zbMath0577.65092OpenAlexW2061297980MaRDI QIDQ1065517

Dirk Roose

Publication date: 1985

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(85)90045-7

zbMATH Keywords

comparison of methodsnonlinear dynamicsdirect methodHopf bifurcation point

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Bifurcations in context of PDEs (35B32)

Related Items (13)

A numerical method for the computation of bifurcation points in fluid mechanics ⋮ Analytical search for bifurcation surfaces in parameter space ⋮ Numerical bifurcation and its application in computation of available transfer capability ⋮ Nonlinear computation ⋮ A method for the numerical computation of Hopf bifurcation ⋮ A numerical algorithm coupling a bifurcating indicator and a direct method for the computation of Hopf bifurcation points in fluid mechanics ⋮ A projective direct method for the computation of hopf bifurcation points ⋮ An Arnoldi-based iterative scheme for nonsymmetric matrix pencils arising in finite element stability problems ⋮ Numerical Optimization Method for Determination of Bifurcation Points and its Application in Stability Analysis of Power System ⋮ Symbolic computation for the qualitative theory of differential equations ⋮ Nonlinear Computation ⋮ Numerical computation of nonsimple turning points and cusps ⋮ A numerical approach to hopf bifurcation points

Uses Software

• AUTO
• LINPACK

Cites Work

• Approximation of Hopf bifurcation
• Numerical computation of periodic orbits that bifurcate from stationary solutions of ordinary differential equations
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• The Hopf bifurcation theorem in infinite dimensions
• Deflation Techniques and Block-Elimination Algorithms for Solving Bordered Singular Systems
• Numerical Computation of Hopf Bifurcation Points for Parabolic Diffusion-Reaction Differential Equations
• The Calculation of Hopf Points by a Direct Method
• The Calculation of Turning Points of Nonlinear Equations
• Algorithm for Evaluation of Complex Bifurcation Points in Ordinary Differential Equations
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