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Replicator Equations and Space
Published online by Cambridge University Press: 28 May 2014
Abstract
A reaction–diffusion replicator equation is studied. A novel method to apply theprinciple of global regulation is used to write down a model with explicit spatialstructure. Properties of stationary solutions together with their stability are analyzedanalytically, and relationships between stability of the rest points of thenon-distributed replicator equation and the distributed system are shown. In particular,we present the conditions on the diffusion coefficients under which the non-distributedreplicator equation can be used to describe the number and stability of the stationarysolutions to the distributed system. A numerical example is given, which shows that thesuggested modeling framework promotes the system’s persistence, i.e., a scenario ispossible when in the spatially explicit system all the interacting species survive whereassome of them go extinct in the non-distributed one.
- Type
- Research Article
- Information
- Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 3: Biological evolution , 2014 , pp. 47 - 67
- Copyright
- © EDP Sciences, 2014
References
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