Snakes, ladders, and breathers: organization of localized patterns in reaction-diffusion systems

DOI10.1137/24M1644328MaRDI QIDQ6667516

Alan R. Champneys, Fahad Al Saadi, Nicolas Verschueren

Publication date: 20 January 2025

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

bifurcationreaction-diffusion systemslocalized pattern

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32) Second-order parabolic systems (35K40) Pattern formations in context of PDEs (35B36)

Cites Work

• Bifurcation structure of dissipative solitons
• Snakes and ladders: localized states in the Swift-Hohenberg equation
• Snaking of radial solutions of the multi-dimensional Swift-Hohenberg equation: a numerical study
• Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
• Exponential asymptotics of localised patterns and snaking bifurcation diagrams
• Control of mitosis by a continuous biochemical oscillation: synchronization; spatially inhomogeneous oscillations
• Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation
• Dissecting the snake: transition from localized patterns to spike solutions
• Bistability, wave pinning and localisation in natural reaction-diffusion systems
• Spatially localized structures in lattice dynamical systems
• On localised hotspots of an urban crime model
• General conditions for Turing and wave instabilities in reaction-diffusion systems
• pde2path -- a Matlab package for continuation and bifurcation in 2D elliptic systems
• Exponential asymptotics of homoclinic snaking
• Pattern Formation and Dynamics in Nonequilibrium Systems
• Snakes, Ladders, and Isolas of Localized Patterns
• Discrete Snaking: Multiple Cavity Solitons in Saturable Media
• To Snake or Not to Snake in the Planar Swift–Hohenberg Equation
• Localized radial solutions of the Swift–Hohenberg equation
• Localized Pattern Formation with a Large-Scale Mode: Slanted Snaking
• Localized Hexagon Patterns of the Planar Swift–Hohenberg Equation
• Reversible Diffeomorphisms and Flows
• Localized structures and front propagation in systems with a conservation law
• Nonlinear PDEs
• A Model for Cell Polarization Without Mass Conservation
• The chemical basis of morphogenesis
• Editorial to Homoclinic snaking at 21: in memory of Patrick Woods
• Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities
• Localized patterns and semi-strong interaction, a unifying framework for reaction–diffusion systems
• Stationary peaks in a multivariable reaction–diffusion system: foliated snaking due to subcritical Turing instability
• Existence of localized radial patterns in a model for dryland vegetation
• Stationary and oscillatory localized patterns in ratio-dependent predator–prey systems
• Three-dimensional spatially localized binary-fluid convection in a porous medium
• Invasion Fronts Outside the Homoclinic Snaking Region in the Planar Swift--Hohenberg Equation
• Localized Radial Roll Patterns in Higher Space Dimensions
• Nonlinear Physics of Ecosystems
• Pattern formation outside of equilibrium
• Localized States in an Extended Swift–Hohenberg Equation
• Degenerate Turing Bifurcation and the Birth of Localized Patterns in Activator-Inhibitor Systems
• Stationary localised patterns without Turing instability
• Time-dependent localized patterns in a predator-prey model
• Amplitude equations for wave bifurcations in reaction-diffusion systems

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