Dissecting the snake: Transition from localized patterns to spike solutions

Desertification by front propagation?

(2017) Yuval R. Zelnik et al.   JOURNAL OF THEORETICAL BIOLOGY

A Model for Cell Polarization Without Mass Conservation

(2017) Nicolas Verschueren et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

From localized spots to the formation of invaginated labyrinthine structures in a Swift–Hohenberg model

(2015) I. Bordeu et al.   Communications in Nonlinear Science and Numerical Simulation

Spatial Localization in Dissipative Systems

(2015) E. Knobloch   Annual Review of Condensed Matter Physics

Chaoticon: localized pattern with permanent dynamics

(2014) N. Verschueren et al.   PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

The Stability of Localized Spot Patterns for the Brusselator on the Sphere

(2014) Ignacio Rozada et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Nonreversible homoclinic snaking

(2013) Jürgen Knobloch et al.   DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL

An Explicit Theory for Pulses in Two Component, Singularly Perturbed, Reaction–Diffusion Equations

(2013) Arjen Doelman et al.   Journal of Dynamics and Differential Equations

On localised hotspots of an urban crime model

(2013) David J.B. Lloyd et al.   PHYSICA D-NONLINEAR PHENOMENA

Predicting the bifurcation structure of localized snaking patterns

(2013) Elizabeth Makrides et al.   PHYSICA D-NONLINEAR PHENOMENA

Analytical Results for Front Pinning between an Hexagonal Pattern and a Uniform State in Pattern-Formation Systems

(2013) G. Kozyreff et al.   PHYSICAL REVIEW LETTERS

Homoclinic Snakes Bounded by a Saddle-Center Periodic Orbit

(2012) A. R. Champneys et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Localized States in an Extended Swift–Hohenberg Equation

(2012) John Burke et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Exponential asymptotics of homoclinic snaking

(2011) A D Dean et al.   NONLINEARITY

Swift-Hohenberg equation with broken cubic-quintic nonlinearity

(2011) S. M. Houghton et al.   PHYSICAL REVIEW E

Dissipative solitons

(2010) H.-G. Purwins et al.   ADVANCES IN PHYSICS

Snaking of radial solutions of the multi-dimensional Swift–Hohenberg equation: A numerical study

(2010) Scott McCalla et al.   PHYSICA D-NONLINEAR PHENOMENA

Defect-mediated snaking: A new growth mechanism for localized structures

(2010) Y.-P. Ma et al.   PHYSICA D-NONLINEAR PHENOMENA

To Snake or Not to Snake in the Planar Swift–Hohenberg Equation

(2010) Daniele Avitabile et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Localized radial solutions of the Swift–Hohenberg equation

(2009) David Lloyd et al.   NONLINEARITY

Swift-Hohenberg equation with broken reflection symmetry

(2009) J. Burke et al.   PHYSICAL REVIEW E

Modulated and Localized States in a Finite Domain

(2009) J. H. P. Dawes   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Snakes, Ladders, and Isolas of Localized Patterns

(2009) Margaret Beck et al.   SIAM JOURNAL ON MATHEMATICAL ANALYSIS

Wave-Pinning and Cell Polarity from a Bistable Reaction-Diffusion System

(2008) Yoichiro Mori et al.   BIOPHYSICAL JOURNAL

A STATISTICAL MODEL OF CRIMINAL BEHAVIOR

(2008) M. B. SHORT et al.   MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES

Exponential asymptotics of localised patterns and snaking bifurcation diagrams

(2008) S.J. Chapman et al.   PHYSICA D-NONLINEAR PHENOMENA

Localized Pattern Formation with a Large-Scale Mode: Slanted Snaking

(2008) J. H. P. Dawes   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Localized Hexagon Patterns of the Planar Swift–Hohenberg Equation

(2008) David J. B. Lloyd et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS