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.
Citation: Alexander S. Bratus, Vladimir P. Posvyanskii, Artem S. Novozhilov. A note on the replicator equation with explicit space and global regulation[J]. Mathematical Biosciences and Engineering, 2011, 8(3): 659-676. doi: 10.3934/mbe.2011.8.659
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.