Abstract.
A model, introduced earlier for the dynamics of a generic efficiency measure in a population of agents by Majumdar and Krapivsky (Phys. Rev. E 63, 054101 (2001)), is investigated on scale-free networks whose degree distribution follows a power law with the tunable exponent γ. The model shows a delocalization transition from a stagnant phase to a growing one when decreasing the degree exponent γ of scale-free networks. By taking into account the specific dynamical properties of the model and the geometrical properties of scale-free networks, we predict the appearance of this critical transition. This work is useful for understanding these kinds of transitions occurring in many dynamical processes on scale-free networks.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S.H. Strogatz, Nature 410, 268 (2001)
N. Goldenfeld, L.P. Kadanoff, Science 284, 87 (1999)
R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)
S.N. Dorogovtsev, J.F.F. Mendes, Adv. Phys. 51, 1079 (2002)
A.-L. Barabási, R. Albert, Science 286, 509 (1999)
D.J. Watts, S.H. Strogatz, Nature 440, 393 (1998)
D.J. Watts, Small Worlds: The Dynamics of Networks Between Order and Randomness (Princeton University Press, New Jersey, 1999)
M.E.J. Newman, C. Moore, D.J. Watts, Phys. Rev. Lett. 84, 3201 (2000)
F. Jasch, A. Blumen, Phys. Rev. E 63, 041108 (2001)
F. Jasch, A. Blumen, J. Chem. Phys. 117, 2474 (2002)
T. Koslowski, M. Koblischke, A. Blumen, Phys. Rev. B 66, 064205 (2002)
R. Pastor-Satorras, A. Vespignani, Phys. Rev. E 63, 066117 (2001)
N. Zekri, J.P. Clerc, Phys. Rev. E 64, 056115 (2001)
M. Kuperman, D.H. Zanette, Eur. Phys. J. B 26, 387 (2002)
S.N. Majumdar, P.L. Krapivsky, Phys. Rev. E 63, 045101 (2001)
S.-Y. Huang, X.-W. Zou, Z.-J. Tan, Z.-G. Shao, Z.-Z. Jin, Phys. Rev. E 68, 016107 (2003)
T. Halpin-Healy, Y.-C. Zhang, Phys. Rep. 254, 215 (1995)
H. Hinrichsen, R. Livi, D. Mukamel, A. Politi, Phys. Rev. Lett. 79, 2710 (1997)
S.N. Majumdar, S. Krishnamurthy, M. Barma, Phys. Rev. E 61, 6337 (2000)
R. Albert, H. Jeong, A.-L. Barabási, Nature 401, 130 (1999)
D. Bulter, Nature 405, 112 (2000)
A. Broder et al., Comput. Networks 33, 309 (2000)
E.W. Zegura, K.L. Calvert, M.J. Donahoo, IEEE/ACM Trans. Network 5, 770 (1997)
M. Faloutsos, P. Faloutsos, C. Faloutsos, Comput. Commun. Rev. 29, 251 (1999)
S. Redner, Eur. Phys. J. B 4, 131 (1998)
M.E.J. Newman, Proc. Natl. Acad. Sci. USA. 98, 404 (2001)
M.E.J. Newman, Phys. Rev. E 64, 016131 (2001)
M.E.J. Newman, Phys. Rev. E 64, 016132 (2001)
H. Jeong, B. Tombor, R. Albert, Z.N. Oltvani, A.-L. Barabási, Nature 407, 651 (2000)
R. Pastor-Satorras, A. Vespignani, Phys. Rev. Lett. 86, 3200 (2001)
K.-I. Goh, D.-S. Lee, B. Kahng, D. Kim, Phys. Rev. Lett. 91, 148701 (2003)
Y. Moreno, A. Vazquez, Europhys. Lett. 57, 765 (2002)
K.-I. Goh, B. Kahng, D. Kim, Phys. Rev. Lett. 87, 278701 (2001)
R. Cohen, S. Havlin, Phys. Rev. Lett. 90, 0588701 (2003)
R. Cohen, K. Erez, D. ben-Avraham, S. Havlin, Phys. Rev. Lett. 85, 4626 (2000)
S.N. Dorogovtsev, J.F.F. Mendes, e-print arXiv:cond-mat/0404593
M.N. Barber, Phase Transitions and Critical Phenomena (Academic Press, New York, 1983)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shao, ZG., Sang, JP., Tan, ZJ. et al. Efficiency dynamics on scale-free networks with tunable degree exponent. Eur. Phys. J. B 48, 587–591 (2005). https://doi.org/10.1140/epjb/e2006-00014-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2006-00014-4