On the Gierer-meinhardt System with Saturation

Global attractivity of equilibrium in GiererMeinhardt system with activator production saturation and gene expression time delays

In thisworkwe investigate a diffusive Gierer–Meinhardt systemwith gene expression time delays in the production of activators and inhibitors, and also a saturation in the activator production, which was proposed by Seirin Lee et al. (2010) [10]. We rigorously consider the basic kinetic dynamics of the Gierer–Meinhardt system with saturation. By using an upper and lower solution method, we show ...

Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions Short title: Gierer-Meinhardt system with Robin boundary conditions

Spikes for the Gierer-meinhardt System in Two Dimensions: the Strong Coupling Case

Numerical computations often show that the Gierer-Meinhardt system has stable solutions which display patterns of multiple interior peaks (often also called spots). These patterns are also frequently observed in natural biological systems. It is assumed that the diffusion rate of the activator is very small and the diffusion rate of the inhibitor is finite (this is the so-called strong-coupling...

Spikes for the Two-dimensional Gierer-meinhardt System: the Strong Coupling Case

Numerical computations often show that the Gierer-Meinhardt system has stable solutions which display patterns of multiple interior peaks (often also called spots). These patterns are also frequently observed in natural biological systems. It is assumed that the diiusion rate of the activator is very small and the diiusion rate of the inhibitor is nite (this is the so-called strong-coupling cas...

Pulses in a Gierer-Meinhardt Equation with a Slow Nonlinearity

In this paper, we study in detail the existence and stability of localized pulses in a GiererMeinhardt equation with an additional ‘slow’ nonlinearity. This system is an explicit example of a general class of singularly perturbed, two component reaction-diffusion equations that goes significantly beyond wellstudied model systems such as Gray-Scott and Gierer-Meinhardt. We investigate the existe...

Identification of Space-Time Distributed Parameters in the Gierer-Meinhardt Reaction-Diffusion System

We consider parameter identification for the classic Gierer-Meinhardt reactiondiffusion system. The original Gierer-Meinhardt model [A. Gierer and H. Meinhardt, Kybernetik, 12 (1972), pp. 30-39] was formulated with constant parameters and has been used as a prototype system for investigating pattern formation in developmental biology. In our paper the parameters are extended in time and space a...