In the nearly seven decades since the publication of Alan Turing's work on morphogenesis,
enormous progress has been made in understanding both the mathematical and biological …

Mathematical and computational models can assist in gaining an understanding of cell
behavior at many levels of organization. Here, we review models in the literature that focus …

In this book we consider solution branches and bifurcations in nonlinear partial differential
equations (PDEs) as models from science (and some economics). Given a nonlinear PDE …

Experimental studies of protein-pattern formation have stimulated new interest in the
dynamics of reaction-diffusion systems. However, a comprehensive theoretical …

Some dividing cells sense their shape by becoming polarized along their long axis. Cell
polarity is controlled in part by polarity proteins, like Rho GTPases, cycling between active …

How does breaking the symmetry of an equation alter the symmetry of its solutions? Here,
we systematically examine how reducing underlying symmetries from spherical to …

A mathematical model connecting epilimnion and hypolimnion is proposed to describe the
competition of phytoplankton for nutrients and light in a stratified lake. The existence and …

Motivated by various physical, cellular and ecological applications, there has been a recent
resurgence of interest in studying the boundary adsorption-desorption of diffusive …

Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in
cell biology, such as cell polarization. Coupled bulk-surface models naturally include …

The formation of protein patterns inside cells is generically described by reaction-diffusion
models. The study of such systems goes back to Turing, who showed how patterns can …