Mutual Invadability Implies Coexistence in Spatial Models

Released on by Richard Durrett
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  • Mutual Invadability Implies Coexistence in Spatial Models Book Detail

  • Author : Richard Durrett
  • Release Date : 2002
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 133
  • ISBN 13 : 0821827685
  • File Size : 49,49 MB
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Mutual Invadability Implies Coexistence in Spatial Models by Richard Durrett PDF Summary

Book Description: In (1994) Durrett and Levin proposed that the equilibrium behavior of stochastic spatial models could be determined from properties of the solution of the mean field ordinary differential equation (ODE) that is obtained by pretending that all sites are always independent. Here we prove a general result in support of that picture. We give a condition on an ordinary differential equation which implies that densities stay bounded away from 0 in the associated reaction-diffusion equation, and that coexistence occurs in the stochastic spatial model with fast stirring. Then using biologists' notion of invadability as a guide, we show how this condition can be checked in a wide variety of examples that involve two or three species: epidemics, diploid genetics models, predator-prey systems, and various competition models.

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The Connective K-Theory of Finite Groups

The Connective K-Theory of Finite Groups

File Size : 89,89 MB
Total View : 8093 Views
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Includes a paper that deals the connective K homology and cohomology of finite groups $G$. This title uses the methods of algebraic geometry to study the ring $