Fractal properties of the lattice Lotka-Volterra model

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 65, Issue 1, 2002, Pages

  Tsekouras, G A ^a,b   Provata, A ^a  

^a INSTITUTE OF NANOSCIENCE AND NANOTECHNOLOGY   (Greece)

^b UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; AUTOMATA THEORY; COMPUTER SIMULATION; FUNCTIONS; PERTURBATION TECHNIQUES; SENSITIVITY ANALYSIS;

ASYMPTOTIC DYNAMICS; BOOLEAN NETWORKS; COMPLEX INTERACTIONS; KAUFFMAN MODELS;

MATHEMATICAL MODELS;

EID: 41349102715     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.016204     Document Type: Article

References (40)

1. G. Nicolis and I. Prigogine, Self-organization in Non-equilibrium Systems (Wiley, New York, 1977).
2. A. Provata, G. Nicolis, and F. Baras, J. Chem. Phys. 110, 8361 (1999).
3. A. Tretyakov, A. Provata, and G. Nicolis, J. Phys. Chem. 99, 2770 (1995).
4. F. Baras, F. Vikas, and G. Nicolis, Phys. Rev. E 60, 3797 (1999).
5. R. Imbihl and G. Ertl, Chem. Rev. 95, 697 (1995).
6. V.P. Zhdanov, Phys. Rev. E 59, 6292 (1999).
7. H. Rose, H. Hempel, and L. Schimanksy-Geier, Physica A 206, 421 (1994).
8. G. Ertl, P.R. Norton, and J. Rustig, Phys. Rev. Lett. 49, 177 (1982).
9. M. Ehsasi, M. Matloch, O. Frank, J.H. Block, K. Christmann, F.S. Rys, and W. Hirschwald, J. Chem. Phys. 91, 4949 (1989).
10. R. Imbihl and G. Ertl, Chem. Rev. 95, 697 (1995).
11. M. Slinko, T. Fink, T. Loher, H.H. Madden, S.J. Lombardo, R. Imbihl, and G. Ertl, Surf. Sci. 264, 157 (1992).
12. C. Voss and N. Kruse, Appl. Surf. Sci. 87/88, 127 (1994).
13. C. Voss and N. Kruse, Ultramicroscopy 73, 211 (1998).
14. N. Hartmann, Y. Kevrekidis, and R. Imbihl, J. Chem. Phys. 112, 6795 (2000).
15. Th. Fink, J.-P. Path, M.R. Basset, R. Imbihl, and G. Ertl, Surf. Sci. 245, 96 (1991).
16. R.M. Ziff, E. Gulari, and Y. Barshad, Phys. Rev. Lett. 56, 2553 (1986).
17. B.J. Brosilow, E. Gulari, and Y. Barshad, J. Chem. Phys. 98, 674 (1993).
18. C.A. Voigt and R.M. Ziff, Phys. Rev. E 56, R6241 (1997).
19. E.V. Albano and J. Marro, J. Chem. Phys. 113, 10279 (2000).
20. P. Meakin, J. Chem. Phys. 93, 2903 (1991).
21. J.W. Evans and M.S. Miesch, Phys. Rev. Lett. 66, 833 (1991).
22. M. Tammaro and J.W. Evans, Phys. Rev. E 52, 2310 (1995).
23. V.P. Zhdanov, Surf. Sci. 426, 345 (1999).
24. D.-J. Liu and J.W. Evans, Phys. Rev. Lett. 84, 955 (2000).
25. V.P. Zhdanov, Phys. Rev. E 60, 7554 (1995).
26. H. Persson, P. Thormwälen, V.P. Zhdanov, and B. Kasemo, Catal. Today 53, 273 (1999).
27. J. D. Murray, Mathematical Biology (Springer-Verlag, Berlin, 1993).
28. P. Grassberger, Math. Biosci. 63, 157 (1983).
29. J.M. Greenberg, B.D. Hassard, and S.P. Hastings, Bull. Am. Math. Soc. 84, 1296 (1978).
30. A.J. Irwin and S.J. Fraser, J. Chem. Phys. 93, 3471 (1990).
31. S. Fraser and R. Kapral, J. Chem. Phys. 85, 5682 (1986).
32. L. Frachebourg, P.L. Krapivsky, and E. Ben-Naim, Phys. Rev. E 54, 6186 (1996).
33. J. W. Turner (private communication).
34. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1983).
35. K. Falconer, Fractal Geometry, Mathematical Foundations and Applications (Wiley, New York, 1990).
36. C. Allain and M. Cloitre, Phys. Rev. A 44, 3552 (1991).
37. R.E. Plotnick, R.H. Gardner, W.W. Hargrove, K. Prestegaard, and M. Perlmutter, Phys. Rev. E 53, 5461 (1996).
38. D.A. Fábio, A. Reis, and R. Riera, J. Phys. A 27, 1827 (1994).
39. F. Esch, S. Günther, E. Schütz, A. Schaak, I.G. Kevrekidis, M. Marsi, M. Kiskinova, and R. Imbihl, Surf. Sci. 443, 245 (1999).
40. M.G. Cosenza and R. Kapral, Phys. Rev. A 46, 1850 (1992).