Kuramoto–Sivashinsky Dynamics on the Center–Unstable Manifold
From MaRDI portal
Publication:4205756
DOI10.1137/0149039zbMath0687.34036OpenAlexW2050973644MaRDI QIDQ4205756
John Guckenheimer, Dieter Armbruster, Philip J. Holmes
Publication date: 1989
Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/0149039
Ordinary differential equations and systems on manifolds (34C40) Bifurcations in context of PDEs (35B32) Local and nonlocal bifurcation theory for dynamical systems (37G99)
Related Items
Chaotic Dynamics in an Integro-Differential Reaction-Diffusion System in the Presence of 0:1:2 Resonance, Collections of heteroclinic cycles in the Kuramoto-Sivashinsky equation, Spatio-temporal coexistence in the cross-diffusion competition system, Control of noisy heteroclinic cycles, Initial conditions for models of dynamical systems, An intrinsic equation of interfacial motion for the solidification of a pure hypercooled melt, Singularities in a modified Kuramoto-Sivashinsky equation describing interface motion for phase transition, The limited effectiveness of normal forms: A critical review and extension of local bifurcation studies of the Brusselator PDE, Wavelet projections of the Kuramoto-Sivashinsky equation. I: Heteroclinic cycles and modulated traveling waves for short systems, Robust heteroclinic cycles, Higher harmonic resonance of two-dimensional disturbances in Rayleigh-Bénard convection, STABILITY AND BIFURCATIONS OF PARAMETRICALLY EXCITED THIN LIQUID FILMS, Archetypal analysis of spatio-temporal dynamics, Local models of spatio-temporally complex fields, Spatio-temporal symmetries and bifurcations via bi-orthogonal decompositions, Unveiling the competitive role of global modes in the pattern formation of rotating sphere flows, Unstable manifolds of relative periodic orbits in the symmetry-reduced state space of the Kuramoto-Sivashinsky system, Modelling the dynamics of nonlinear partial differential equations using neural networks, Forced symmetry breaking of homoclinic cycles in a PDE with O(2) symmetry, Symmetries and dynamics for 2-D Navier-Stokes flow, Interaction of adjacent bursts in the wall region, Local bifurcations in the periodic boundary value problem for the generalized Kuramoto-Sivashinsky equation, A generalized sideband stability theory via center manifold projection, Second-kind equilibrium states of the Kuramoto-Sivashinsky equation with homogeneous Neumann boundary conditions, Convergence of a finite difference scheme for a flame/smoldering-front evolution equation and its application to wavenumber selection, Dynamics and control of the modified generalized Korteweg-de Vries-Burgers equation with periodic boundary conditions, Local attractors of one of the original versions of the Kuramoto-Sivashinsky equation, Linearized Stability of Partial Differential Equations with Application to Stabilization of the Kuramoto--Sivashinsky Equation, A single bounded input‐feedback control to the generalized Korteweg–de Vries–Burgers–Kuramoto–Sivashinsky equation, The existence of intrinsic rotating wave solutions of a flame/smoldering-front evolution equation, Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations, On symmetric long-wave patterns in two-layer flows, Low-dimensional models of thin film fluid dynamics., Thin liquid films on a slightly inclined heated plate, Preserving dissipation in approximate inertial forms for the Kuramoto- Sivashinsky equation, Fixed points of a destabilized Kuramoto-Sivashinsky equation, Analysis of Kuramoto-Sivashinsky Model of Flame/Smoldering Front by Means of Curvature Driven Flow, Suppression of bursting, Minimal dynamial systems from PDEs using Sobolev eigenfunctions, Stability enhancement by boundary control in the Kuramoto-Sivashinsky equation, Reconstructing phase space from PDE simulations, Heteroclinic cycles and modulated travelling waves in a system with \(D_ 4\) symmetry, Robust heteroclinic cycles in the one-dimensional complex Ginzburg-Landau equation, Reduced-order-based feedback control of the Kuramoto--Sivashinsky equation, Nonlinear interaction of four electrostatic waves in a plasma, Intermittent dynamics in simple models of the turbulent wall layer, Phase-space analysis of bursting behavior in Kolmogorov flow, Low dimensional models of the wall region in a turbulent boundary layer: new results, Spanwise pairing of finite-amplitude longitudinal vortex rolls in inclined free-convection boundary layers, Numerical analysis of a weighted-residual integral boundary-layer model for nonlinear dynamics of falling liquid films, Nonlinear adaptive boundary control of the modified generalized Korteweg-de Vries-Burgers equation, Bifurcation phenomena in a convection problem with temperature dependent viscosity at low aspect ratio, Organization of spatially periodic solutions of the steady Kuramoto-Sivashinsky equation, Noise induced intermittency in a model of a turbulent boundary layer, THE OSEBERG TRANSITION: VISUALIZATION OF GLOBAL BIFURCATIONS FOR THE KURAMOTO–SIVASHINSKY EQUATION, ROBUST HETEROCLINIC CYCLES IN TWO-DIMENSIONAL RAYLEIGH–BÉNARD CONVECTION WITHOUT BOUSSINESQ SYMMETRY, Spatiotemporal pattern extraction by spectral analysis of vector-valued observables, Variational approach to closure of nonlinear dynamical systems: autonomous case, Local bifurcations in the Cahn-Hilliard and Kuramoto-Sivashinsky equations and in their generalizations, Instabilities of one-dimensional cellular patterns, A note on the computation of bifurcation diagrams of the Kuramoto- Sivashinsky equation by pseudospectral methods, On the relation between low-dimensional models and the dynamics of coherent structures in the turbulent wall layer, Numerical Computations and Computer Assisted Proofs of Periodic Orbits of the Kuramoto--Sivashinsky Equation, Modelling and nonlinear boundary stabilization of the modified generalized Korteweg-de Vries-Burgers equation, Instability in the nebula model of compressive viscous gases, Computational efficiency and approximate inertial manifolds for a Bénard convection system