Nonequilibrium critical behavior of a species coexistence model

Statistical and Nonlinear Physics

Abstract.

A biologically motivated model for spatio-temporal coexistence of two competing species is studied by mean-field theory and numerical simulations. In d ≥2 dimensions the phase diagram displays an extended region where both species coexist, bounded by two second-order phase transition lines belonging to the directed percolation universality class. The two transition lines meet in a multicritical point, where a non-trivial critical behavior is observed.

PACS.

87.23.Cc Population dynamics and ecological pattern formation 05.70.Ln Nonequilibrium and irreversible thermodynamics 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions  

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References

  1. J. Marro, R. Dickman, Nonequilibrium phase transitions in lattice models (Cambridge University Press, Cambridge, 1999) Google Scholar
  2. W. Kinzel, Z. Phys. B 58, 229 (1985) CrossRefMathSciNetGoogle Scholar
  3. H. Hinrichsen, Adv. Phys. 49, 815 (2000) CrossRefADSGoogle Scholar
  4. G. Ódor, Rev. Mod. Phys. 76, 663 (2004) CrossRefADSGoogle Scholar
  5. S. Lübeck, Int. J. Mod. Phys. B 18, 3977 (2004) CrossRefADSGoogle Scholar
  6. H.K. Janssen, Z. Phys. B 42, 151 (1981) CrossRefGoogle Scholar
  7. P. Grassberger, Z. Phys. B 47, 365 (1982) CrossRefMathSciNetGoogle Scholar
  8. H.-K. Janssen, U.C. Täuber, Ann. Phys. (NY) 315, 147 (2005) MATHCrossRefADSMathSciNetGoogle Scholar
  9. R.M. Ziff, E. Gulari, Y. Barshad, Phys. Rev. Lett. 56, 2553 (1986) CrossRefADSGoogle Scholar
  10. G. Grinstein, Z.W. Lai, D.A. Browne, Phys. Rev. A 40, 4820 (1989) CrossRefADSGoogle Scholar
  11. I. Jensen, H.C. Fogedby, R. Dickman, Phys. Rev. A 41, 3411 (1990) CrossRefADSGoogle Scholar
  12. I. Jensen, Phys. Rev. Lett. 70, 1465 (1993) CrossRefADSGoogle Scholar
  13. M.A. Muñoz, G. Grinstein, R. Dickman, R. Livi, Phys. Rev. Lett. 76, 451 (1996) CrossRefADSGoogle Scholar
  14. U.C. Täuber, M.J. Howard, H. Hinrichsen, Phys. Rev. Lett. 80, 2165 (1998) CrossRefADSGoogle Scholar
  15. Y.Y. Goldschmidt, H. Hinrichsen, M.J. Howard, U.C. Täuber, Phys. Rev. E 59, 6381 (1999) CrossRefADSMathSciNetGoogle Scholar
  16. K.E. Bassler, D.A. Browne, Phys. Rev. Lett. 77, 4094 (1996) CrossRefADSGoogle Scholar
  17. L. Canet, H. Chaté, B. Delamotte, Phys. Rev. Lett. 92, 255703 (2004) CrossRefADSGoogle Scholar
  18. D. Tilman, P. Karveia, Spatial Ecology: The Role of Space in Popolation Dynamics and Inter-specific Interactions (Princeton University Press, Princeton USA, 1997) Google Scholar
  19. S.C. Palmer, R.A. Norton, Biochemical systematics and ecology 20, 219 (1992) CrossRefGoogle Scholar
  20. I. Schön, R.K. Butlin, H.I. Griffiths, K. Martens, Proc. R. Soc. Lond. B 265, 235 (1997) Google Scholar
  21. H.J. Muller, Mut. Res. 1, 29 (1964) Google Scholar
  22. T.E. Harris, Ann. Prob. 2, 969 (1974) MATHGoogle Scholar
  23. I. Jensen, R. Dickman, J. Stat. Phys. 71, 89 (1993) MATHCrossRefADSGoogle Scholar
  24. R. Dickman, Phys. Rev. E 60, 2441 (1999) CrossRefADSGoogle Scholar
  25. S. Lübeck, R.D. Willmann, Nuclear Physics B 718, 341 (2005); S. Lübeck, Int. J. Mod. Phys. B 18, 3977 (2004) CrossRefADSMathSciNetGoogle Scholar
  26. H. Hinrichsen, H.M. Koduvely, Eur. Phys. J. B 5, 257 (1998) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  • H. Reinhardt
    • 1
  • F. Böhm
    • 1
  • B. Drossel
    • 1
  • H. Hinrichsen
    • 2
  1. 1.Institut für FestkörperphysikDarmstadtGermany
  2. 2.Fakultät für Physik und Astronomie, Universität WürzburgWürzburgGermany

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