Unified framework for localized patterns in reaction–diffusion systems; the Gray–Scott and Gierer–Meinhardt cases

Spikes and localised patterns for a novel Schnakenberg model in the semi-strong interaction regime

(2021) FAHAD AL SAADI et al.   EUROPEAN JOURNAL OF APPLIED MATHEMATICS

Dissecting the snake: Transition from localized patterns to spike solutions

(2021) Nicolas Verschueren et al.   PHYSICA D-NONLINEAR PHENOMENA

Stationary and oscillatory localized patterns in ratio-dependent predator–prey systems

(2021) Fahad Al Saadi et al.   IMA JOURNAL OF APPLIED MATHEMATICS

Localized patterns and semi-strong interaction, a unifying framework for reaction–diffusion systems

(2021) Fahad Al Saadi et al.   IMA JOURNAL OF APPLIED MATHEMATICS

Localised structures in a virus-host model

(2021) Fahad Al Saadi et al.   JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Pattern Dynamics in a Diffusive Gierer–Meinhardt Model

(2020) Mengxin Chen et al.   INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

Bistability, wave pinning and localisation in natural reaction–diffusion systems

(2020) Alan R. Champneys et al.   PHYSICA D-NONLINEAR PHENOMENA

Destabilization Mechanisms of Periodic Pulse Patterns Near a Homoclinic Limit

(2018) Arjen Doelman et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Spot Dynamics in a Reaction-Diffusion Model of Plant Root Hair Initiation

(2018) Daniele Avitabile et al.   SIAM JOURNAL ON APPLIED MATHEMATICS

Spatially localized structures in the Gray–Scott model

(2018) Punit Gandhi et al.   PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

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

Localized states qualitatively change the response of ecosystems to varying conditions and local disturbances

(2016) Yuval R. Zelnik et al.   Ecological Complexity

After 1952: The later development of Alan Turing's ideas on the mathematics of pattern formation

(2016) Jonathan H.P. Dawes   HISTORIA MATHEMATICA

Breathing pulses in singularly perturbed reaction-diffusion systems

(2015) Frits Veerman   NONLINEARITY

Stripe to Spot Transition in a Plant Root Hair Initiation Model

(2015) V. F. Bren͂a--Medina et al.   SIAM JOURNAL ON APPLIED MATHEMATICS

Spatial Localization in Dissipative Systems

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

Beyond Turing: The response of patterned ecosystems to environmental change

(2014) Koen Siteur et al.   Ecological Complexity

Mathematical Modeling of Plant Root Hair Initiation: Dynamics of Localized Patches

(2014) V. Bren͂a--Medina et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

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

Asymptotic and Bifurcation Analysis of Wave-Pinning in a Reaction-Diffusion Model for Cell Polarization

(2011) Yoichiro Mori et al.   SIAM JOURNAL ON APPLIED MATHEMATICS

A Theoretical Model for ROP Localisation by Auxin in Arabidopsis Root Hair Cells

(2009) Robert J. H. Payne et al.   PLoS One

Snakes, Ladders, and Isolas of Localized Patterns

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

Front motion and localized states in an asymmetric bistable activator-inhibitor system with saturation

(2008) Arik Yochelis et al.   PHYSICAL REVIEW E

Localized Hexagon Patterns of the Planar Swift–Hohenberg Equation

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