Spatially localized structures in dissipative systems: open problems
From MaRDI portal
Publication:5458161
DOI10.1088/0951-7715/21/4/T02zbMath1139.35002MaRDI QIDQ5458161
Publication date: 11 April 2008
Published in: Nonlinearity (Search for Journal in Brave)
nonlinear opticsneurobiologyfluid flowdissipative solitonssurface catalysisbuckling of slender structures
Nonlinear parabolic equations (35K55) Developmental biology, pattern formation (92C15) Bifurcations in context of PDEs (35B32) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02)
Related Items
Continuation and bifurcation in nonlinear PDEs - algorithms, applications, and experiments ⋮ The Lefever-Lejeune nonlinear lattice: convergence dynamics and the structure of equilibrium states ⋮ Existence and stability of spatially localized patterns ⋮ Transition to turbulence in shear flows ⋮ Multiple localized states in centrifugally stable rotating flow ⋮ Mechanisms of vegetation-ring formation in water-limited systems ⋮ On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular ⋮ Defect-mediated snaking: a new growth mechanism for localized structures ⋮ Bifurcation analysis to the Lugiato-Lefever equation in one space dimension ⋮ Two-dimensional localized structures in harmonically forced oscillatory systems ⋮ Regime shifts in models of dryland vegetation ⋮ Pattern formation -- a missing link in the study of ecosystem response to environmental changes ⋮ Discontinuous shock solutions of the Whitham modulation equations as zero dispersion limits of traveling waves ⋮ Isolas of 2-pulse solutions in homoclinic snaking scenarios ⋮ CRIME HOTSPOT EMERGENCE IN MEXICO CITY: A COMPLEXITY SCIENCE PERSPECTIVE ⋮ Spatio-temporal numerical solutions of the coupled real and complex Ginzburg-Landau amplitude equations for one-dimensional systems near the Turing-Hopf bifurcation ⋮ Localized Turing patterns in nonlinear optical cavities ⋮ On localised hotspots of an urban crime model ⋮ Beyond all order asymptotics for homoclinic snaking in a Schnakenberg system ⋮ Multistability in Ecosystems: Concerns and Opportunities for Ecosystem Function in Variable Environments ⋮ Logarithmic expansions and the stability of periodic patterns of localized spots for reaction-diffusion systems in \(\mathbb R^2\) ⋮ Snakes and isolas in non-reversible conservative systems ⋮ Localized edge states nucleate turbulence in extended plane Couette cells ⋮ Exploiting the Hamiltonian structure of a neural field model ⋮ Analysis of spatial patterns in a vegetation model ⋮ Magnetohydrodynamic convectons ⋮ Transitions and heteroclinic cycles in the general Gierer-Meinhardt equation and cardiovascular calcification model ⋮ Snaking of radial solutions of the multi-dimensional Swift-Hohenberg equation: a numerical study ⋮ Spatial instabilities untie the exclusion-principle constraint on species coexistence ⋮ Invasion Fronts Outside the Homoclinic Snaking Region in the Planar Swift--Hohenberg Equation ⋮ Exponential asymptotics of localised patterns and snaking bifurcation diagrams ⋮ Localised radial patterns on the free surface of a ferrofluid ⋮ Stability on time-dependent domains ⋮ Traveling Pulse Solutions in a Three-Component FitzHugh--Nagumo Model ⋮ Snakes in square, honeycomb and triangular lattices ⋮ Nonlinear Forecasting of the Generalized Kuramoto–Sivashinsky Equation ⋮ A New Resonance Mechanism in the Swift--Hohenberg Equation with Time-Periodic Forcing ⋮ Orientation-Dependent Pinning and Homoclinic Snaking on a Planar Lattice ⋮ Numerical Results for Snaking of Patterns over Patterns in Some 2D Selkov--Schnakenberg Reaction-Diffusion Systems ⋮ Interaction between vegetation patches and gaps: a self-organized response to water scarcity ⋮ Turbulent spots in a channel: large-scale flow and self-sustainability
Uses Software