The present review summarizes experimental and theoretical work dealing with self-
organized solitary localized structures (LSs) that are observed in spatially extended …

This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

One of the major challenges in modern biology is to understand how the molecular
components of a living cell operate in a highly noisy environment. What are the specific …

In this paper we introduce a conceptual model for vegetation patterns that generalizes the
Klausmeier model for semi-arid ecosystems on a sloped terrain (Klausmeier in Science 284 …

A recent study of canonical activator-inhibitor Schnakenberg-like models posed on an
infinite line is extended to include models, such as Gray–Scott, with bistability of …

In the limit of small activator diffusivity ɛ, the stability of symmetric k-spike equilibrium
solutions to the Gierer-Meinhardt reaction-diffusion system in a one-dimensional spatial …

The dynamics and stability of multispot patterns to the Gray–Scott (GS) reaction-diffusion
model in a two-dimensional domain is studied in the singularly perturbed limit of small …

Asymmetric spike patterns are constructed for the two‐component Schnakenburg reaction–
diffusion system in the singularly perturbed limit of a small diffusivity of one of the …

We investigate an SIRS epidemic model with spatial diffusion and nonlinear incidence rates.
We show that for small diffusion rate of the infected class D_ I DI, the infected population …

The existence, stability, and pulse-splitting behavior of spike patterns in the one-dimensional
Gray–Scott model on a finite domain is analyzed in the semi-strong spike-interaction regime …