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 Coexistence and critical behavior in a lattice model of competing species
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/6213

title: Coexistence and critical behavior in a lattice model of competing species
authors: Wendykier, Jacek
Lipowski, Adam
Ferreira, Antonio Luis
issue date: 2011
publisher: American Physical Society
abstract: In the present paper we study a lattice model of two species competing for the same resources. Monte Carlo simulations for d = 1,2, and 3 show that when resources are easily available both species coexist. However, when the supply of resources is on an intermediate level, the species with slower metabolism becomes extinct. On the other hand, when resources are scarce it is the species with faster metabolism that becomes extinct. The range of coexistence of the two species increases with dimension. We suggest that our model might describe some aspects of the competition between normal and tumor cells. With such an interpretation, examples of tumor remission, recurrence, and different morphologies are presented. In the d = 1 and d = 2 models, we analyze the nature of phase transitions: they are either discontinuous or belong to the directed-percolation universality class, and in some cases they have an active subcritical phase. In the d = 2 case, one of the transitions seems to be characterized by critical exponents that differ from directed-percolation ones, but this transition could be also weakly discontinuous. In the d = 3 version, Monte Carlo simulations are in a good agreement with the solution of the mean-field approximation. This approximation predicts that oscillatory behavior occurs in the present model but only for d greater than or similar to 2. For d >= 2, a steady state depends on the initial configuration in some cases.
URI: http://hdl.handle.net/10773/6213
ISSN: 1539-3755
publisher version/DOI: link.aps.org/doi/10.1103/PhysRevE.83.031904
source: Physical Review E
appears in collectionsFIS - Artigos

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