Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds

History dependence and the continuum approximation breakdown: the impact of domain growth on Turing’s instability

(2017) Václav Klika et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

A Trace Finite Element Method for PDEs on Evolving Surfaces

(2017) Maxim A. Olshanskii et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A Turing–Hopf Bifurcation Scenario for Pattern Formation on Growing Domains

(2016) Jorge A. Castillo et al.   BULLETIN OF MATHEMATICAL BIOLOGY

The dynamics of localized spot patterns for reaction-diffusion systems on the sphere

(2016) Philippe H Trinh et al.   NONLINEARITY

Computing with Functions in Spherical and Polar Geometries I. The Sphere

(2016) Alex Townsend et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Explicitly Solvable Nonlocal Eigenvalue Problems and the Stability of Localized Stripes in Reaction-Diffusion Systems

(2016) I. Moyles et al.   STUDIES IN APPLIED MATHEMATICS

High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals

(2016) Luciano Marcon et al.   eLife

The Control of Growth Symmetry Breaking in the Arabidopsis Hypocotyl

(2015) Alexis Peaucelle et al.   CURRENT BIOLOGY

Positional information and reaction-diffusion: two big ideas in developmental biology combine

(2015) J. B. A. Green et al.   DEVELOPMENT

Stability analysis and simulations of coupled bulk-surface reaction-diffusion systems

(2015) A. Madzvamuse et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces

(2014) A. Madzvamuse et al.   PHYSICAL REVIEW E

Bifurcation analysis of reaction–diffusion Schnakenberg model

(2013) Ping Liu et al.   JOURNAL OF MATHEMATICAL CHEMISTRY

Simple computation of reaction–diffusion processes on point clouds

(2013) Colin B. Macdonald et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Anisotropic growth shapes intestinal tissues during embryogenesis

(2013) M. Ben Amar et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

An Extension of Chebfun to Two Dimensions

(2013) Alex Townsend et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Finite element methods for surface PDEs

(2013) Gerhard Dziuk et al.   ACTA NUMERICA

Characterization of turing diffusion-driven instability on evolving domains

(2012) Georg Hetzer et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Turing's model for biological pattern formation and the robustness problem

(2012) P. K. Maini et al.   Interface Focus

The surface finite element method for pattern formation on evolving biological surfaces

(2011) R. Barreira et al.   JOURNAL OF MATHEMATICAL BIOLOGY

The Gierer–Meinhardt system on a compact two-dimensional Riemannian manifold: Interaction of Gaussian curvature and Green's function

(2010) Wang Hung Tse et al.   JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

(2009) Anotida Madzvamuse et al.   JOURNAL OF MATHEMATICAL BIOLOGY

Turning a plant tissue into a living cell froth through isotropic growth

(2009) F. Corson et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Patterns on growing square domains via mode interactions

(2008) Adela Comanici et al.   DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL

Root growth in Arabidopsis requires gibberellin/DELLA signalling in the endodermis

(2008) Susana Ubeda-Tomás et al.   NATURE CELL BIOLOGY

Dynamics of anisotropic tissue growth

(2008) Thomas Bittig et al.   NEW JOURNAL OF PHYSICS