Mathematical Biosciences and Engineering, 2011, 8(3): 659-676. doi: 10.3934/mbe.2011.8.659.

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A note on the replicator equation with explicit space and global regulation

1. Applied Mathematics–1, Moscow State University of Railway Engineering, Obraztsova 9, Moscow, 127994

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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Keywords evolutionary stable state; reaction-diffusion systems.; Nash equilibrium; Replicator equation

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


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