Pulses in a Gierer-Meinhardt Equation with a Slow Nonlinearity

Semistrong Pulse Interactions in a Class of Coupled Reaction-Diffusion Equations

Pulse-pulse interactions play central roles in a variety of pattern formation phenomena, including self-replication. In this article, we develop a theory for the semistrong interaction of pulses in a class of singularly perturbed coupled reaction-diffusion equations that includes the (generalized) Gierer– Meinhardt, Gray–Scott, Schnakenberg, and Thomas models, among others. Geometric conditions...

Nonlinear Asymptotic Stability of the Semistrong Pulse Dynamics in a Regularized

We use renormalization group (RG) techniques to prove the nonlinear asymptotic stability for the semistrong regime of two-pulse interactions in a regularized Gierer–Meinhardt system. In the semistrong limit the localized activator pulses interact strongly through the slowly varying inhibitor. The interaction is not tail-tail as in the weak interaction limit, and the pulse amplitudes and speeds ...

Nonlinear Asymptotic Stability of the Semistrong Pulse Dynamics in a Regularized Gierer-Meinhardt Model

We use renormalization group (RG) techniques to prove the nonlinear asymptotic stability for the semi-strong regime of two-pulse interactions in a regularized Gierer-Meinhardt system. In the semi-strong limit the localized activator pulses interact strongly through the slowly varying inhibitor. The interaction is not tail-tail as in the weak interaction limit, and the pulse amplitudes and speed...

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

Local Stability of Spike Steady States in a Simplified Gierer-meinhardt System

In this paper we study the stability of the single internal spike solution of a simplified Gierer-Meinhardt’ system of equations in one space dimension. The linearization around this spike consists of a selfadjoint differential operator plus a non-local term, which is a non-selfadjoint compact integral operator. We find the asymptotic behaviour of the small eigenvalues and we prove stability of...