Phase transitions and spatio-temporal fluctuations in stochastic lattice lotka-volterra models

Journal of Statistical Physics

Volumn 128, Issue 1-2, 2007, Pages 447-483

  Mobilia, Mauro ^a,b   Georgiev, Ivan T ^b,c   Täuber, Uwe C ^b  

^a UNIVERSITY OF MUNICH   (Germany)

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^c Integrated Finance Limited   (United States)

Author keywords

Nonequilibrium phase transitions; Population dynamics; Spatio temporal patterns; Stochastic fluctuations

Indexed keywords

EID: 34249903336     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-006-9146-3     Document Type: Conference Paper

References (69)

1. A. J. Lotka, Proc. Natl. Acad. Sci. U.S.A. 6:410 (1920);
2. J. Amer. Chem. Soc. 42:1595 (1920).
3. V. Volterra, Mem. Accad. Lincei 2:31 (1926);
4. Leçons sur la théorie mathématique de la lutte pour la vie (Gauthiers-Villars, Paris, 1931).
5. Theoretical Ecology, edited by R. M. May (Sinauer Associates, Sunderland, 1981);
6. Population Regulation and Dynamics, Proceedings of a Royal Society discussion meeting, edited by M. P. Kassel and R. M. May. The Royal Society, London (1990);
7. R. M. May, Stability and Complexity in Model Ecosystems (Princeton University Press, Princeton, 1973).
8. H. Haken, Synergetics. 3rd ed., (Springer-Verlag, New York, 1983).
9. D. Neal, Introduction to Population Biology (Cambridge University Press, Cambridge, 2004).
10. J. Maynard Smith, Models in Ecology (Cambridge University Press, Cambridge, 1974).
11. J. D. Murray, Mathematical Biology Vols. I and II (Springer-Verlag, New York, 2002).
12. A. N. Kolmogorov, Sulla Teoria di Volterra della Lotta per 1'Esistezza. Giorn. Instituto Ital. Attuari 7:74-80 (1936).
13. N. S. Goel, S. C. Maitra and E. W. Montroll, Rev. Mod. Phys. 43:231 (1971).
14. G. Picard and T. W. Watson, Phys. Rev. Lett. 48:1610 (1982).
15. J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics (Cambridge University Press, Cambridge, 1998).
16. R. M. May and W. Leonard, SIAM J. Appl. Math. 29:243 (1975).
17. R. Durrett, SIAM Rev. 41:677 (1999).
18. C. Elton and M. Nicholson, J. Anim. Ecol 11:215 (1942).
19. P. Rohani, R. M. May and M. P. Hassell, J. Theor. Biol. 181:97 (1996);
20. Modeling Spatiotemporal Dynamics in Ecology, edited by J. Bascompte and R. V. Solé, (Springer, 1998).
21. J. E. Satulovsky and T. Tomé, Phys. Rev. E 49:5073 (1994).
22. A. Lipowski and D. Lipowska, Physica A 276:456 (2000);
23. A. Lipowski, Phys. Rev. E 60:5179 (1999);
24. Kowalick, A. Lipowski, and A. L. Ferreira, ibid. 66:066107 (2002).
25. T. Antal and M. Droz, Phys. Rev. E 63:056119 (2001).
26. A. J. McKane and T. J. Newman, Phys. Rev. Lett. 94:218102 (2005).
27. S. R. Dunbar, J. Math. Biol. 17:11 (1983);
28. Trans. Amer. Math. Soc. 268:557 (1984).
29. A. Provata, G. Nicolis and F. Baras, J. Chem. Phys. 110:8361 (1999);
30. G. A. Tsekouras and A. Provata, Phys. Rev. E 65:016204 (2001).
31. H. Matsuda, N. Ogita, A. Sasaki and K. Satö, Prog. Theor. Phys. 88:1035 (1992).
32. L. Frachebourg and P. L. Krapivsky, J. Phys. A 31:L287 (1998);
33. Frachebourg, P. L. Krapivsky, and E. Ben-Naim, Phys. Rev. E 54:6186 (1996);
34. Phys. Rev. Lett. 77:2125 (1996);
35. G. Szabó and T. C. Czáran, Phys. Rev. E 63:061904 (2001);
36. ibid. 64:042902 (2002);
37. G. Szabó and G. A. Sznaider, ibid. 69:031911 (2004).
38. E. Bettelheim, O. A. Nadav, and N. M. Shnerb, Physica E 9:600 (2001);
39. N. M. Shnerb and O. Agam, e-print cond-mat/9903408.
40. N. Boccara, O. Roblin and M. Roger, Phys. Rev. E 50:4531 (1994).
41. A. F. Rozenfeld and E. V. Albano, Physica A 266:322 (1999);
42. R. Monetti, A. F. Rozenfeld and E. V. Albano, Physica A 283:52 (2000);
43. A. F. Rozenfeld and E. V. Albano, Phys. Rev. E 63:061907 (2001);
44. A. F. Rozenfeld and E. V. Albano, Phys. Lett. A 332:361 (2004).
45. M. Droz and A. Pekalski, Phys. Rev. E 63:051909 (2001).
46. W. Kinzel, Percolation structures and concepts. Ann. Israel Phys. Soc. 5:425 (1983);
47. P. Grassberger, J. Phys. A 29:7013 (1996).
48. H. Hinrichsen, Adv. Phys. 49:815 (2000);
49. H. K. Janssen and U. C. Täuber, Ann. Phys. (NY) 315:147 (2005).
50. H. K. Janssen, J. Stat. Phys. 103:801 (2001).
51. M. Mobilia, I. T. Georgiev and U. C. Täuber, Phys. Rev. E 73:040903(R) (2006); e-print:q-bio.PE/0508043.
52. D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations. 3rd ed., (Oxford University Press, Oxford, 1999).
53. J. Riordan, C. R. Doering and D. ben-Avraham, Phys. Rev. Lett. 75:565 (1995).
54. L. Pechenik and H. Levine, Phys. Rev. E 59:3893 (1999).
55. Y. Fujii and M. Wadati, J. Phys. Soc. Jpn 66:3770 (1997);
56. Mobilia and P.-A. Bares, Phys. Rev. E 63:036121(2001).
57. Nonequilibrium Statistical Mechanics in One Dimension, edited by V Privman. Cambridge University Press, Cambridge, (1997);
58. F. C. Alcaraz, M. Droz, M. Henkel and V Rittenberg, Ann. Phys. (N.Y.) 230:250 (1994);
59. Henkel, E. Orlandini and J. Santos, ibid. 259:163 (1997);
60. C. Mattis andM. L. Glasser, Rev. Mod. Phys. 70:979 (1998).
61. B. Schmittmann and R. K. P. Zia, in: Phase Transitions and Critical Phenomena, Vol. 17, edited by C. Domb and J. L. Lebowitz (Academic Press, New York, 1995).
62. Two movies ('L256.mpg' and 'L512.mpg') corresponding to the situation of Fig. 2 (but with A. = 2.1 and lattice sizes 256 × 256 and 512 × 512), as well as one movie ('movie3.mpg') corresponding to the situation of Fig. 3 (but with A. = 0.18 and lattice size 256 × 256) can be found at http:// www.phys.vt.edu/~tauber/PredatorPray/movies/.
63. H. K. Janssen, Z Phys. B 42:151 (1981);
64. P. Grassberger, Z Phys. B 47:365 (1982).
65. U. C. Täuber, M. T. Howard, and B. P. Vollmayr-Lee, J. Phys. A: Math. Gen. 38:R79 (2005).
66. G. Odor and N. Menyhárd, Physica D 168:305 (2002).
67. O. Deloubrière, H. J. Hilhorst, and U. C. Täuber, Phys. Rev. Lett. 89:250601 (2002);
68. H. J. Hilhorst, O. Deloubrière, M. J. Washenberger, and U. C. Täuber, J. Phys. A: Math. Gen. 37:7063 (2004).
69. F. van Wijland, Phys. Rev. E 63:022101 (2001).