Clustering, advection, and patterns in a model of population dynamics with neighborhood-dependent rates

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 70, Issue 1 2, 2004, Pages

  Hernández García, Emilio ^a   López, Cristóbal ^a  

^a UNIVERSITAT DE LES ILLES BALEARS   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

DENSITY (SPECIFIC GRAVITY); FLOW OF FLUIDS; MARKOV PROCESSES; MATHEMATICAL MODELS; POPULATION STATISTICS; PROBABILITY; REACTION KINETICS;

ADVECTION; FOCK SPACES; PARTICLE DENSITY; POPULATION DYNAMICS;

HIGH ENERGY PHYSICS;

EID: 45849155761     PISSN: 15393755     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.70.016216     Document Type: Article

References (39)

1. J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, 1998).
2. W. R. Young, A. J. Roberts, and G. Stuhne, Nature (London) 412, 328 (2001); W. R. Young, in Proceedings of the 12th 'Aha Huliko'a Hawaiian Winter Workshop (University of Hawaii, Manoa, 2001).
3. W. R. Young, A. J. Roberts, and G. Stuhne, Nature (London) 412, 328 (2001); W. R. Young, in Proceedings of the 12th 'Aha Huliko'a Hawaiian Winter Workshop (University of Hawaii, Manoa, 2001).
4. R. Adler, in Proceedings of the 10th 'Aha Huliko'a Hawaiian Winter Workshop (University of Hawaii, Manoa, 1997).
5. A. M. Etheridge, An Introduction to Superprocesses (American Mathematical Society, New York,. 2000).
6. Y-C. Zhang, M. Serva, and M. Polikarpov, J. Stat. Phys. 58, 849 (1990).
7. B. Houchmandzadeh, Phys. Rev. E 66, 052902 (2002).
8. M. Meyer, S. Havlin, and A. Bunde, Phys. Rev. E 54, 5567 (1996).
9. J. Cardy, in The Mathematical Beauty of Physics, edited by J. M. Drouffe and J. B. Zuber (World Scientific, Singapore, 1996).
10. N. M. Shnerb, Y. Louzoun, E. Bettelheim, and S. Solomon, Proc. Natl. Acad. Sci. U.S.A. 97, 10322 (2000).
11. A. P. Martin, K. J. Richards, A. Provenzale, and A. Bracco, Global Biogeochem. Cycles 16:10.1029/2001GB001449 (2002).
12. A. P. Martin, Prog. Oceanogr. 57, 125 (2003).
13. M. A. Fuentes, M. N. Kuperman, and V. M. Kenkre, Phys. Rev. Lett. 91, 158104 (2003).
14. A. Sasaki, J. Theor. Biol. 186, 415 (1997).
15. H. Sayama, M. A. M. de Aguiar, Y. Bar-Yam, and M. Baranger, Phys. Rev. E 65, 051919 (2002).
16. J. Billingham, Nonlinearity 17, 313 (2004).
17. G. Flierl, D. Grunbaum, S. Levin, and D. Olson, J. Theor. Biol. 196, 397 (1999).
18. A. Mogilner and L. Edelstein-Keshet, J. Math. Biol. 38, 534 (1999); A. Mogilner, L. Edelstein-Keshet, L. Bent, and A. Spiros, ibid. 47, 353 (2003).
19. A. Mogilner and L. Edelstein-Keshet, J. Math. Biol. 38, 534 (1999); A. Mogilner, L. Edelstein-Keshet, L. Bent, and A. Spiros, ibid. 47, 353 (2003).
20. J. L. Boldrini et al., J. Theor. Biol. 185, 523 (1997); L. Allen and E. J. Allen, Bull. Math. Biol. 58, 815 (1996).
21. J. L. Boldrini et al., J. Theor. Biol. 185, 523 (1997); L. Allen and E. J. Allen, Bull. Math. Biol. 58, 815 (1996).
22. C. Escudero, J. Buceta, F. J. de la Rubia, and Katja Lindenberg, Phys. Rev. E 69, 021908 (2004).
23. This is asynchronous updating. In this simple BB model, the order of the updating (synchronous, asynchronous, sequential) is irrelevant, but it is important in the neighborhood dependent models.
24. H. Hinrichsen, Adv. Phys. 49, 815 (2000).
25. E. Moro, Phys. Rev. E 68, 025102(R) (2003).
26. J. Cardy and U. C. Täuber, Phys. Rev. Lett. 77, 4780 (1996); J. Stat. Phys. 90, 1 (1998).
27. J. Cardy and U. C. Täuber, Phys. Rev. Lett. 77, 4780 (1996); J. Stat. Phys. 90, 1 (1998).
28. J. Kockelkoren and H. Chaté, Phys. Rev. Lett. 90, 125701 (2003).
29. G. Grinstein and M. A. Muñoz, in Fourth Granada Lectures in Computational Physics, edited by P. L. Garrido and J. Marro (Springer, Berlin, 1997).
30. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
31. M. Doi, J. Phys. A 9, 1465 (1979); L. Peliti, J. Phys. (France) 46, 1469 (1985).
32. M. Doi, J. Phys. A 9, 1465 (1979); L. Peliti, J. Phys. (France) 46, 1469 (1985).
33. The following references contain short and useful summaries of the technique: L. Pechenik and H. Levine, Phys. Rev. E 59, 3893 (1999); E. Bettelheim, O. Agam, and N. M. Shnerb, Physica E (Amsterdam) 9, 600 (2001); A. Kamenev, in Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems, NATO Science Series II, Vol. 72, edited by I. V. Lerner, B. L. Altshuler, V. I. Falko, and T. Giamarchi (Kluwer, Dordrecht, 2002).
34. The following references contain short and useful summaries of the technique: L. Pechenik and H. Levine, Phys. Rev. E 59, 3893 (1999); E. Bettelheim, O. Agam, and N. M. Shnerb, Physica E (Amsterdam) 9, 600 (2001); A. Kamenev, in Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems, NATO Science Series II, Vol. 72, edited by I. V. Lerner, B. L. Altshuler, V. I. Falko, and T. Giamarchi (Kluwer, Dordrecht, 2002).
35. The following references contain short and useful summaries of the technique: L. Pechenik and H. Levine, Phys. Rev. E 59, 3893 (1999); E. Bettelheim, O. Agam, and N. M. Shnerb, Physica E (Amsterdam) 9, 600 (2001); A. Kamenev, in Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems, NATO Science Series II, Vol. 72, edited by I. V. Lerner, B. L. Altshuler, V. I. Falko, and T. Giamarchi (Kluwer, Dordrecht, 2002).
36. C. W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences (Springer, New York, 1985).
37. M. Droz and A. McKane, J. Phys. A 27, L467 (1994).
38. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 1993).
39. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford University Press, Oxford, 1997).