Hopf bifurcation at a degenerate stationary pitchfork
DOI10.1016/0362-546X(86)90132-XzbMath0594.34042OpenAlexW2060344386MaRDI QIDQ3724741
Publication date: 1986
Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0362-546x(86)90132-x
small perturbationsparabolic differential equationsfirst order differential equationbifurcating stationary solutionshighly degenerate singularity
Nonlinear parabolic equations (35K55) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Equations involving nonlinear operators (general) (47J05) Periodic solutions to ordinary differential equations (34C25) Local and nonlocal bifurcation theory for dynamical systems (37G99) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)
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Cites Work
- On the principle of reduced stability
- Hopf bifurcation for ordinary differential equations with a zero eigenvalue
- Classification and unfoldings of degenerate Hopf bifurcations
- Degenerate bifurcation at simple eigenvalues and stability of bifurcating solutions
- Imperfect bifurcation in the presence of symmetry
- Coincident bifurcation of equilibrium and periodic solutions of evolution equations
- Smooth functions invariant under the action of a compact Lie group
- The Hopf bifurcation theorem in infinite dimensions
- Hopf bifurcation at multiple eigenvalues
- Stability of bifurcating solutions by Leray-Schauder degree
- Periodic and Steady-State Mode Interactions Lead to Tori
- Hopf bifurcation from a turning point.
- Bifurcation formulas for O.D.E.'S in n
- Generalized Hopf bifurcation in Hilbert space
- Existence of small periodic solutions of ordinary differential equations in \(\mathbb{R}^2\)
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