A note on the replicator equation with explicit space and global regulation - Alexander S. Bratus; Vladimir P. Posvyanskii; Artem S. Novozhilov (Mathematical Biosciences and Engineering)
A replicator equation with explicit space and global regulation is considered. This model provides a naturalframework to follow frequencies of species that are distributed in the space. For this model, analogues to classical notions of the Nash equilibrium and evolutionary stable state are provided. A sufficient condition for a uniform stationary state to be a spatially distributed evolutionary stable state is presented and illustrated with examples.