title: A note on the replicator equation with explicit space and global regulation.
abstract: A replicator equation with explicit space and global regulation is considered. This model provides a natural framework 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.
authors.affiliation: Applied Mathematics-1, Moscow State University of Railway Engineering, Obraztsova 9, Moscow, 127994, Russia. alexander.bratus@yandex.ru
authors.forename: Alexander S
authors.initials: AS
authors.lastname: Bratus
authors.forename: Vladimir P
authors.initials: VP
authors.lastname: Posvyanskii
authors.forename: Artem S
authors.initials: AS
authors.lastname: Novozhilov
mesh_terms: D000818:Animals; D005075:Biological Evolution; D003198:Computer Simulation; D017753:Ecosystem; D025461:Feedback, Physiological / Q000502:physiology*; D006801:Humans; D008954:Models, Biological; D011158:Population Growth