THE OSEBERG TRANSITION: VISUALIZATION OF GLOBAL BIFURCATIONS FOR THE KURAMOTO–SIVASHINSKY EQUATION

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

Mathematics Subject Classification ID

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

This page was built for publication: THE OSEBERG TRANSITION: VISUALIZATION OF GLOBAL BIFURCATIONS FOR THE KURAMOTO–SIVASHINSKY EQUATION