Origin of power-law distributions in deterministic walks: The influence of landscape geometry

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

Volumn 75, Issue 6, 2007, Pages

  Santos, M C ^a   Boyer, D ^b   Miramontes, O ^b   Viswanathan, G M ^c   Raposo, E P ^d   Mateos, J L ^b   Da Luz, M G E ^a  

^a FEDERAL UNIVERSITY OF PARANÁ   (Brazil)

^b UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^c FEDERAL UNIVERSITY OF ALAGOAS   (Brazil)

^d FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; DYNAMICAL SYSTEMS; INVARIANCE; POLYNOMIAL APPROXIMATION; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING;

DYNAMICAL TRAPPING MECHANISM; LOCOMOTION RULE; POWER-LAW DISTRIBUTIONS;

RANDOM PROCESSES;

EID: 34547304145     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.75.061114     Document Type: Article

References (46)

1. R. Metzler and J. Klafter, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3 339, 1 (2000);
2. R. Metzler and J. Klafter, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/37/31/R01 37, R161 (2004).
3. G. M. Zaslavsky, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(02)00331- 9 371, 461 (2002).
4. I. Peterson, The Jungle of Randomness: A Mathematical Safari (Wiley, New York, 1998).
5. Lévy Flights and Related Topics in Physics, edited by, M. F. Shlesinger, G. M. Zaslavsky, and, U. Frisch, (Springer, Berlin, 1995).
6. C. Tsallis, Phys. World PHWOEW 0953-8585 10, 42 (1997).
7. J. Klafter and I. M. Sokolov, Phys. World PHWOEW 0953-8585 18, 29 (2005).
8. A. I. Saichev and S. G. Utkin, J. Exp. Theor. Phys. JTPHES 1063-7761 10.1134/1.1800201 99, 443 (2004);
9. G. M. Viswanathan, E. P. Raposo, F. Bartumeus, J. Catalan, and M. G. E. da Luz, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.011111 72, 011111 (2005).
10. B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, New York, 1983).
11. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.59.381 59, 381 (1987);
12. P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.38.364 38, 364 (1988).
13. M. Paczuski, S. Maslov, and P. Bak, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.53.414 53, 414 (1996).
14. M. A. Zaks, Physica A PHYADX 0378-4371 310, 285 (2002).
15. B. J. West, P. Grigolini, R. Metzler, and T. F. Nonnenmacher, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.55.99 55, 99 (1997).
16. B. Podobnik, P. C. Ivanov, Y. Lee, A. Chessa, and H. E. Stanley, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2000-00540-7 50, 711 (2000);
17. M. J. Keeling, Theor Popul. Biol. ZZZZZZ 0040-5809 58, 21 (2000).
18. M. Levy and S. Solomon, Int. J. Mod. Phys. C IJMPEO 0129-1831 10.1142/S0129183196000491 7, 595 (1996);
19. M. Levy and S. Solomon, Int. J. Mod. Phys. C IJMPEO 0129-1831 10.1142/S0129183196000624 7, 745 (1996);
20. D. Sornette and R. Cont, J. Phys. I JPGCE8 1155-4304 10.1051/jp1:1997169 7, 431 (1997).
21. P. M. de Oliveira, Theory Biosci. THBIFM 1431-7613 10.1078/1431-7613- 00023 120, 1 (2001);
22. T. Gisiger, Biol. Rev. Cambridge Philos. Soc. BRCPAH 0006-3231 10.1017/S1464793101005607 76, 161 (2001);
23. R. E. Ulanowicz, BioSystems BSYMBO 0303-2647 64, 13 (2002);
24. M. F. Shlesinger and J. Klafter, in On Growth and Form, edited by, H. E. Stanley, and, N. Ostrowsky, (Nijhoff, Dordrecht, 1986);
25. D. W. Stephens and J. R. Krebs, Foraging Theory (Princeton University Press, Princeton, 1987).
26. G. M. Viswanathan, S. V. Buldyrev, S. Havlin, M. G. E. da Luz, E. P. Raposo, and H. E. Stanley, Nature (London) NATUAS 0028-0836 10.1038/44831 401, 911 (1999).
27. E. P. Raposo, S. V. Buldyrev, M. G. E. da Luz, M. C. Santos, H. E. Stanley, and G. M. Viswanathan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.240601 91, 240601 (2003).
28. M. C. Santos, E. P. Raposo, G. M. Viswanathan, and M. G. E. da Luz, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2004-10114-9 67, 734 (2004).
29. G. Ramos-Fernandez and B. Ayala-Orozco, in Primates in Fragments: Ecology and Conservation, edited by, L. K. Marsh, (Kluwer Academic Press, New York, 2002);
30. G. Ramos-Fernandez, J. L. Mateos, O. Miramontes, G. Cocho, H. Larralde, and B. Ayala-Orozco, Behav. Ecol. Sociobiol. BESOD6 0340-5443 10.1007/s00265-003-0700-6 55, 223 (2004);
31. D. Boyer, G. Ramos-Fernandez, O. Miramontes, J. L. Mateos, G. Cocho, H. Larralde, H. Ramos, and F. Rojas, Proc. R. Soc. London, Ser. B PRLBA4 0962-8452 10.1098/rspb.2005.3462 273, 1743 (2006).
32. A. M. Reynolds, Phys. Lett. A PYLAAG 0375-9601 360, 224 (2006).
33. G. Oshanin, H. S. Wio, K. Lindenberg, and S. F. Burlatsky, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/19/6/065142 19, 065142 (2007).
34. O. Bénichou, C. Loverdo, M. Moreau, and R. Voituriez, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/19/6/065141 19, 065141 (2007).
35. M. C. Santos, G. M. Viswanathan, E. P. Raposo, and M. G. E. da Luz, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.046143 72, 046143 (2005).
36. C. L. Faustino, L. R. da Silva, M. G. E. da Luz, E. P. Raposo, and G. M. Viswanathan, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/77/30002 77, 30002 (2007).
37. G. F. Lima, A. S. Martinez, and O. Kinouchi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.010603 87, 010603 (2001);
38. C. A. S. Terçariol and A. S. Martinez, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.021103 72, 021103 (2005);
39. S. Risau-Gusman, A. S. Martinez, and O. Kinouchi, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.016104 68, 016104 (2003).
40. H. Freund and P. Grassberger, Physica A PHYADX 0378-4371 10.1016/0378-4371(92)90033-M 190, 218 (1992);
41. D. Gale, J. Propp, S. Sutherland, and S. Troubetzkoy, Math. Intell. MAINDC 0343-6993 17, 48 (1995);
42. L. A. Bunimovich, Asterisque ZZZZZZ 0303-1179 286, 231 (2003);
43. D. Boyer and H. Larralde, Complexity COMPFS 1076-2787 10.1002/cplx.20068 10, 52 (2005).
44. L. A. Bunimovich, Physica D PDNPDT 0167-2789 10.1016/j.physd.2003.09.028 187, 20 (2004).
45. D. Boyer, O. Miramontes, G. Ramos-Fernández, J. L. Mateos, and G. Cocho, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.04.091 342, 329 (2004).
46. J. C. Cressoni, M. A. A. da Silva, and G. M. Viswanathan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.070603 98, 070603 (2007).