MBE
A note on the replicator equation with explicit space and global regulation
Alexander S. Bratus Vladimir P. Posvyanskii Artem S. Novozhilov
Mathematical Biosciences & Engineering 2011, 8(3): 659-676 doi: 10.3934/mbe.2011.8.659
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.
keywords: evolutionary stable state reaction-diffusion systems. Nash equilibrium Replicator equation

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