Nonlinear Convective Instability of Turing-Unstable Fronts near Onset: A Case Study

@article{Ghazaryan2007NonlinearCI,
  title={Nonlinear Convective Instability of Turing-Unstable Fronts near Onset: A Case Study},
  author={Anna Ghazaryan and Bj{\"o}rn Sandstede},
  journal={SIAM J. Applied Dynamical Systems},
  year={2007},
  volume={6},
  pages={319-347}
}
Fronts are travelling waves in spatially extended systems that connect two different spatially homogeneous rest states. If the rest state behind the front undergoes a supercritical Turing instability, then the front will also destabilize. On the linear level, however, the front will be only convectively unstable since perturbations will be pushed away from the front as it propagates. In other words, perturbations may grow but they can do so only behind the front. The goal of this paper is to… CONTINUE READING