THE OSEBERG TRANSITION: VISUALIZATION OF GLOBAL BIFURCATIONS FOR THE KURAMOTO–SIVASHINSKY EQUATION
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Publication:5474152
DOI10.1142/S0218127401001979zbMath1090.35506OpenAlexW2021617431MaRDI QIDQ5474152
Ioannis G. Kevrekidis, Mark E. Johnson, Michael S. Jolly
Publication date: 23 June 2006
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0218127401001979
KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Bifurcations in context of PDEs (35B32) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10)
Related Items (8)
STABILITY AND BIFURCATIONS OF PARAMETRICALLY EXCITED THIN LIQUID FILMS ⋮ A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS ⋮ High-dimensional chaotic saddles in the Kuramoto-Sivashinsky equation ⋮ Analysis of chaotic saddles in high-dimensional dynamical systems: The Kuramoto–Sivashinsky equation ⋮ The Kuramoto-Sivashinsky equation revisited: low-dimensional corresponding systems ⋮ The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques ⋮ A geometric method for infinite-dimensional chaos: symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line ⋮ Finite element approximation of invariant manifolds by the parameterization method
Cites Work
- Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations
- Local and global behavior near homoclinic orbits
- Gevrey class regularity and approximate inertial manifolds for the Kuramoto-Sivashinsky equation
- Approximate inertial manifolds of exponential order
- Two-dimensional invariant manifolds and global bifurcations: Some approximation and visualization studies
- Local models of spatio-temporally complex fields
- Inertial manifolds for the Kuramoto-Sivashinsky equation
- Collections of heteroclinic cycles in the Kuramoto-Sivashinsky equation
- Back in the Saddle Again: A Computer Assisted Study of the Kuramoto–Sivashinsky Equation
- Traveling waves on fluid interfaces: Normal form analysis of the Kuramoto–Sivashinsky equation
- On Flame Propagation Under Conditions of Stoichiometry
- Travelling-waves of the Kuramoto-Sivashinsky, equation: period-multiplying bifurcations
- Kuramoto–Sivashinsky Dynamics on the Center–Unstable Manifold
- Two-dimensional global manifolds of vector fields
- Deterministic Nonperiodic Flow
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