The purpose of the present paper is to investigate the pattern formation and secondary
instabilities, including Eckhaus instability and zigzag instability, of an activator–inhibitor …

As a classical activator-inhibitor system with diffusion effects, the Gierer–Meinhardt (GM)
model has received a considerable attention in recent years. Discussions on dynamic …

A depletion-type reaction-diffusion Gierer-Meinhardt model with Langmuir-Hinshelwood
reaction scheme and the homogeneous Neumann boundary conditions is introduced and …

Localized spatial patterns commonly occur for various classes of linear and nonlinear
diffusive processes. In particular, localized spot patterns, where the solution concentrates at …

In this paper we consider the 2-component reaction–diffusion model that was recently
obtained by a systematic reduction of the 3-component Gilad et al. model for dryland …

Collective organisation of patterns into ring-like configurations has been well-studied when
patterns are subject to either weak or semi-strong interactions. However, little is known …

Gierer–Meinhardt system is a molecularly plausible model to describe pattern formation.
When gene expression time delay is added, the behavior of the Gierer–Meinhardt model …

We study the spectrum of a new class of nonlocal eigenvalue problems (NLEPs) that
characterize the linear stability properties of localized spike solutions to the singularly …

Using the solutions of an elliptic system and an ODE system, under certain conditions, we
get the explicit solution to the following initial–boundary value problem of Gierer-Meinhardt …