Normal forms for parametrized vector fields and its application to bifurcations of some reaction diffusion equations

DOI10.1007/BF03167061zbMath0635.35006MaRDI QIDQ3774211

Hiroshi Kokubu

Publication date: 1984

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

zbMATH Keywords

Hopf bifurcationbifurcationsevolution equationscenter manifold theorynormal form theoryreaction diffusiondoubly degenerate singularityparameter dependencesparametrized vector fields

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Periodic solutions to PDEs (35B10) Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32)

Related Items

Normal forms for an age structured model, Bogdanov-Takens bifurcation in a predator-prey model with age structure, Normal forms for semilinear equations with non-dense domain with applications to age structured models, Normal forms of vector fields with perturbation parameters and their application, Hopf bifurcation for a susceptible-infective model with infection-age structure

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bifurcation analysis near a double eigenvalue of a model chemical reaction
• Applications of centre manifold theory
• 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
• Singularities of vector fields
• Non-linear semi-groups
• Diffusion induced chaos
• Normal forms for singularities of vector fields
• A theory for imperfect bifurcation via singularity theory
• LECTURES ON BIFURCATIONS IN VERSAL FAMILIES
• Generic bifurcations of varieties