Dynamics of metastable localized patterns and its application to the interaction of spike solutions for the Gierer-Meinhardt systems in two spatial dimensions
The authors investigate the so-called Gierer-Meinhardt system describing pattern formation in the regeneration of hydra amenable. They prove the existence and stability of a single spike solution. They also investigate the interaction of multi-spike solutions in two spatial dimensions when the distances between them are sufficiently large. It explains and clarifies a part of mechanism of the evolution process of localized patterns observed in simulations of the Gierer-Meinhardt model.
scientific article; zbMATH DE number 1802940