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

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  • 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.
    Mathematics Subject Classification: Primary: 35K57, 35B35, 91A22; Secondary: 92D25.


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