A note on the replicator equation with explicit space and global regulation
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Published on: April 27, 2021
Alexander S Bratus1, Vladimir P Posvyanskii, Artem S Novozhilov
1Applied Mathematics-1, Moscow State University of Railway Engineering, Obraztsova 9, Moscow, 127994, Russia. alexander.bratus@yandex.ru
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.
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