Localized patterns in planar bistable weakly coupled lattice systems

DOI10.1088/1361-6544/ab7d1ezbMath1447.37065OpenAlexW3033279761MaRDI QIDQ5113437

Björn Sandstede, Jason J. Bramburger

Publication date: 11 June 2020

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1361-6544/ab7d1e

zbMATH Keywords

Lyapunov-Schmidt reductionlattice dynamical systembistable systemsnaking bifurcationlocalized pattern

Mathematics Subject Classification ID

Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Pattern formations in context of PDEs (35B36)

Related Items (7)

Approximate localised dihedral patterns near a turing instability ⋮ Snakes on Lieb lattice ⋮ Spatially localized structures in lattice dynamical systems ⋮ Language competition on lattices ⋮ Pattern Formation in Random Networks Using Graphons ⋮ Dynamics of waves and patterns. Abstracts from the workshop held August 8--14, 2021 (hybrid meeting) ⋮ Isolas of multi-pulse solutions to lattice dynamical systems

Cites Work

• Snaking and isolas of localised states in bistable discrete lattices
• Snakes and ladders: localized states in the Swift-Hohenberg equation
• Snaking of radial solutions of the multi-dimensional Swift-Hohenberg equation: a numerical study
• Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices
• Existence and stability of spatially localized patterns
• Mechanisms of vegetation-ring formation in water-limited systems
• Pattern formation on the free surface of a ferrofluid: spatial dynamics and homoclinic bifurcation
• Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation
• Spatially localized structures in lattice dynamical systems
• Isolas versus snaking of localized rolls
• Isolas of 2-pulse solutions in homoclinic snaking scenarios
• On localised hotspots of an urban crime model
• Predicting the bifurcation structure of localized snaking patterns
• Asymptotics beyond all orders and Stokes lines in nonlinear differential-difference equations
• The emergence of a coherent structure for coherent structures: localized states in nonlinear systems
• Pattern Formation
• Snakes, Ladders, and Isolas of Localized Patterns
• To Snake or Not to Snake in the Planar Swift–Hohenberg Equation
• Localized radial solutions of the Swift–Hohenberg equation
• Localized Hexagon Patterns of the Planar Swift–Hohenberg Equation
• Hotspot formation and dynamics for a continuum model of urban crime
• Snakes and isolas in non-reversible conservative systems
• Non-reversible perturbations of homoclinic snaking scenarios
• Snakes in square, honeycomb and triangular lattices
• Orientation-Dependent Pinning and Homoclinic Snaking on a Planar Lattice
• Existence of Symmetric and Asymmetric Spikes for a Crime Hotspot Model

This page was built for publication: Localized patterns in planar bistable weakly coupled lattice systems