4 papers
Travelling front solutions in a spatially heterogeneous reaction-diffusion system
M. Chirilus-Bruckner, L. van Vianen, F. Veerman
We investigate a two-component reaction-diffusion system with a slow-fast structure and spatially varying coefficients and appearing in the slow equation. Under mild bo…
Pattern formation in a Swift-Hohenberg equation with spatially periodic coefficients
Jolien Kamphuis, Martina Chirilus-Bruckner
We study the Swift-Hohenberg equation - a paradigm model for pattern formation - with "large" spatially periodic coefficients and find a Turing bifurcation that generates patterns…
Stability of Breathers for a Periodic Klein-Gordon Equation
Martina Chirilus-Bruckner, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis
The existence of breather type solutions, i.e., periodic in time, exponentially localized in space solutions, is a very unusual feature for continuum, nonlinear wave type equations…
Chaotic motion and singularity structures of front solutions in multi-component FitzHugh-Nagumo-type systems
Martina Chirilus-Bruckner, Peter van Heijster, Jens D. M. Rademacher
We study the dynamics of front solutions in a certain class of multi-component reaction-diffusion systems, where one fast component governed by an Allen-Cahn equation is weakly cou…