Synchronizability of chaotic logistic maps in delayed complex networks

European Physical Journal B

Volumn 67, Issue 1, 2009, Pages 83-93

  Ponce C , M ^a   Masoller, C ^b   Martí, Arturo C ^a  

^a INSTITUTO DE FÍSICA   (Uruguay)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

AVERAGE NUMBERS; CHAOTIC LOGISTIC MAPS; COMPLEX NETWORKS; COMPLEX SYSTEMS; COUPLED LOGISTIC MAPS; COUPLING STRENGTHS; DELAY DISTRIBUTIONS; DELAY TIME; GLOBAL INDICATORS; HETEROGENEOUS DELAYS; INFLUENCE OF FEEDBACKS; LOCAL DYNAMICS; NEAREST NEIGHBORS; NETWORK CONNECTIVITIES; NETWORK SIZES; OSCILLATORY DYNAMICS; SCALE-FREE; SELF FEEDBACKS; SMALL NETWORKS; SMALL WORLDS; SYNCHRONIZABILITY; TIME-DEPENDENT STATE; TWO REGIMES; WEAK COUPLINGS;

DYNAMICS; OPTICAL PROJECTORS; TOPOLOGY;

CHAOTIC SYSTEMS;

EID: 60349089317     PISSN: 14346028     EISSN: 14346036     Source Type: Journal    
DOI: 10.1140/epjb/e2008-00467-3     Document Type: Article

References (48)

1. S.H. Strogatz, Nature 410, 268 (2001)
2. See the special issue Pramana J. Phys. 70, 1 (2008): Proceedings of the Conference and Workshop on Perspectives in Nonlinear Dynamics (2007)
3. J.M. Montoya, S.L. Pimm, R.V. Sole, Nature 442, 259 (2006)
4. D. Garlaschelli, G. Caldarelli, L. Pietronero, Nature 423, 165 (2003)
5. H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai, A.L. Barabasi, Nature 407, 651 (2000)
6. N. Barkai, S. Leibler, Nature 387, 913 (1997)
7. C.S. Zhou, L. Zemanova, G. Zamora, et al., Phys. Rev. Lett. 97, 238103 (2006)
8. V.M. Eguiluz, D.R. Chialvo, G.A. Cecchi, M. Baliki, A.V. Apkarian, Phys. Rev. Lett. 94, 018102 (2005)
9. M. Kuperman, G. Abramson, Phys. Rev. Lett. 86, 2909 (2001)
10. S. Eubank, H. Guclu, V.S.A. Kumar, M.V. Marathe, A. Srinivasan, Z. Toroczkai, N. Wang, Nature 429, 180 (2004)
11. R. Albert, H. Jeong, A.L. Barabasi, Nature 406, 378 (2000)
12. G. Palla, I. Derenyi, I. Farkas, T. Vicsek, Nature 435, 814 (2005)
13. J.M. Kumpula, J.P. Onnela, J. Saramaki et al., Phys. Rev. Lett. 99, 228701 (2007)
14. J.M. Buldu, P. Cano, M. Koppenberger, J.A. Almendral, S. Boccaletti, New J. Phys. 9, 172 (2007)
15. N.J. Guido, X. Wang, D. Adalsteinsson, D. McMillen, J. Hasty, C.R. Cantor, T.C. Elston, J.J. Collins, Nature 439, 856 (2006)
16. G.M. Suel, J. Garcia-Ojalvo, L.M. Liberman, M.B. Elowitz, Nature 440, 545 (2006)
17. R. Guimera, L.A.N. Amaral, Nature 433, 895 (2005)
18. S.C. Manrubia, A.S. Mikbailov, D.H. Zanette, Emergence, of Dynamical Order. Synchronization Phenomena in Complex Systems (World Scientific, Singapore, 2004)
19. A.E. Motter, C. Zhou, J. Kurths, Phys. Rev. E 71, 016116 (2005)
20. M. Chavez, D.U. Hwang, A. Amann, H.G.E. Hentschel, S. Boccaletti, Phys. Rev. Lett. 94, 218701 (2005)
21. C.S. Zhou, J. Kurths, Phys. Rev. Lett. 96, 164102 (2006)
22. T. Nishikawa, A.E. Motter, Y.C. Lai et al, Phys. Rev. Lett. 91, 014101 (2003)
23. F.M. Atay, J. Jost, A. Wende, Phys. Rev. Lett. 92, 144101 (2004)
24. R.M. May, Nature 261, 459 (1976)
25. The logistic map captures two key effects in population dynamics: (i) grow (the reproduction of a population will increase at a rate proportional to the present population size when the population size is small) and (ii) starvation (the growth rate will decrease at a rate proportional to the value obtained by taking the "carrying capacity" of the environment less the population size). The Logistic Map displays, depending on a parameter (which represents the combined rate for reproduction and starvation), either population extinction, stable population, periodic or chaotic oscillations
26. C. Masoller, A.C. Marti, Phys. Rev. Lett. 94, 134102 (2005)
27. A.C. Marti, M. Ponce, C. Masoller, Physica A 371, 104 (2006)
28. M.E.J. Newman, D.J. Watts, Phys. Rev. E 60, 7332 (1999);
29. M.E.J. Newman, D.J. Watts, Phys. Lett. A 263, 341 (1999)
30. R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)
31. M.G. Rosenblum, A.G. Pikovsky, Phys. Rev. Lett. 92, 114102 (2004)
32. O.V. Popovych, V. Krachkovskyi, P.A. Tass, Int. J. Bif. Chaos 17, 2517 (2007)
33. E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Kbaykovieb, I. Kanter, Phys. Rev. E 76, 066214 (2006)
34. I.B. Schwartz, L.B. Shaw, Phys. Rev. E 75, 046207 (2007)
35. T. Omi, S. Shinomoto, Phys. Rev. E 77, 046214 (2008)
36. A.C. Marti, M. Ponce, C. Masoller, Phys. Rev. E 72, 066217 (2005)
37. X. Gong, S. Guan, X. Wang, C.-H. Lai, Phys. Rev. E 77, 056212 (2008)
38. R. Morgado, M. Ciesla, L. Longa, F.A. Oliveira, Europhys. Lett. 79, 10002 (2007)
39. S. Kim, S.H. Park, C.S. Ryu, Phys. Rev. Lett. 79, 2911 (1997)
40. A. Roxin, N. Brunel, D. Hansel, Phys. Rev. Lett. 94, 238103 (2005)
41. P.G. Lind, A. Nunes, J.A.C. Gallas, Physica A 371, 100 (2006)
42. R.L. Viana, C. Grebogi, S.E. de S. Pinto, S.R. Lopes, A.M. Batista, J. Kurths, Physica, D 206, 94 (2005)
43. E. Ullner, A. Zaikin, E.I. Volkov, J. Garcia-Ojalvo, Phys. Rev. Lett. 99, 148103 (2007)
44. S. Jalan, J. .lost, F.M. Atay, Chaos 16, 033124 (2006)
45. C. Masoller, A.C. Marti, D.H. Zanette, Physica A 325, 186 (2003)
46. C.M. Gonzalez, C. Masoller, C. Torrent, J. Garcia-Ojalvo, Europhys. Lett. 79, 64003 (2007)
47. J.R. Sanchez, R. Lopez-Ruiz, Physica A 355, 633 (2005)
48. O.A. Rosso, H.A. Larrondo, M.T. Martin, A. Piastino, M.A. Fuentes, Phys. Rev. Lett. 99, 154102 (2007)