Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl


Preferences help
enabled [disable] Abstract
Number of results


2009 | 7 | 3 | 421-431

Article title

Superstatistics and renewal critical events


Title variants

Languages of publication



An approach to intermittent systems based on renewal processes is reviewed. The Waiting Times (WTs) between events are the main variables of interest in intermittent systems. A crucial role is played by the class of critical events, characterized by Non-Poisson statistics and non-exponential WT distribution. A particular important case is given by WT distributions with power tail. Critical events play a crucial role in the behavior of a property known as Renewal Aging. Focusing on the role of critical events, the relation between superstatistics and non-homogeneous Poisson processes is discussed, and the role of Renewal Aging is illustrated by comparing a Non-Poisson model with a Poisson one, both of them modulated by a periodic forcing. It is shown that the analysis of Renewal Aging is sensitive to the presence of critical events and that this property can be exploited to detect Non-Poisson statistics in a time series. As a consequence, it is claimed that, apart from the characterization of superstatistical features such as the distribution of the intensive parameter or the separation of the time scales, the Renewal Aging property can give some effort to better determine the role of Non-Poisson critical events in intermittent systems.


  • Istituto di Scienze dell’Atmosfera e del Clima (ISAC-CNR), Strada Provinciale Lecce-Monteroni Km 1.200, I-73100, Lecce, Italy
  • Istituto di Scienze dell’Atmosfera e del Clima (ISAC-CNR), Strada Provinciale Lecce-Monteroni Km 1.200, I-73100, Lecce, Italy


  • [1] C. Beck, Phys. Rev. Lett. 87, 180601 (2001) http://dx.doi.org/10.1103/PhysRevLett.87.180601[Crossref]
  • [2] C. Beck, Continuum Mech. Therm. 16, 293 (2004) http://dx.doi.org/10.1007/s00161-003-0145-1[Crossref]
  • [3] E. G. D. Cohen, Physica D 193(1–4), 35 (2004) http://dx.doi.org/10.1016/j.physd.2004.01.007[Crossref]
  • [4] C. Beck, Physica D 193(1–4), 195 (2004) http://dx.doi.org/10.1016/j.physd.2004.01.020[Crossref]
  • [5] C. Beck, Europhys. Lett. 64(2), 151 (2003) http://dx.doi.org/10.1209/epl/i2003-00498-4[Crossref]
  • [6] S. Abe, C. Beck, E. G. D. Cohen, Phys. Rev. E 76, 031102 (2007) http://dx.doi.org/10.1103/PhysRevE.76.031102[Crossref]
  • [7] T. Zhou, F. Moss, P. Jung, Phys. Rev. A 42, 3161 (1990) http://dx.doi.org/10.1103/PhysRevA.42.3161[Crossref]
  • [8] A. Longtin, A. Bulsara, F. Moss, Phys. Rev. Lett. 67, 656 (1991) http://dx.doi.org/10.1103/PhysRevLett.67.656[Crossref]
  • [9] E. Barkai, Y. Jung and R.J. Silbey, Annu. Rev. Phys. Chem. 55, 457 (2004) http://dx.doi.org/10.1146/annurev.physchem.55.111803.143246[Crossref]
  • [10] G. Baldini, F. Cannone, G. Chirico, Science 309, 1096 (2005) http://dx.doi.org/10.1126/science.1115001[Crossref]
  • [11] S. Bianco, P. Grigolini, P. Paradisi, Chem. Phys. Lett. 438, 336 (2007) http://dx.doi.org/10.1016/j.cplett.2007.03.013[Crossref]
  • [12] M. Kuno, D. P. Fromm, H.F. Hamann, A. Gallagher, D. J. Nesbitt, J. Chem. Phys. 112, 3117 (2000) http://dx.doi.org/10.1063/1.480896[Crossref]
  • [13] P. Paradisi, P. Allegrini, F. Barbi, S. Bianco, P. Grigolini, AIP Conf. Proc. 800, 92 (2005) http://dx.doi.org/10.1063/1.2138599[Crossref]
  • [14] S. Bianco, P. Grigolini, P. Paradisi, J. Chem. Phys. 123, 174704 (2005) http://dx.doi.org/10.1063/1.2102903[Crossref]
  • [15] D. R. Cox, Renewal Theory (Chapman and Hall, New York, 1967)
  • [16] P. Allegrini, F. Barbi, P. Grigolini, P. Paradisi, Phys. Rev. E 73, 046136 (2006) http://dx.doi.org/10.1103/PhysRevE.73.046136[Crossref]
  • [17] P. Allegrini, F. Barbi, P. Grigolini, P. Paradisi, Chaos Soliton. Fract. 34, 11 (2007) http://dx.doi.org/10.1016/j.chaos.2007.01.045[Crossref]
  • [18] L. Devroye, Non-uniform random variate generation (Springer-Verlag, New York, 1986)
  • [19] P. Paradisi, P. Grigolini, S. Bianco, O. C. Akin, Int. J. Bifurcat. Chaos 18, 2681 (2008) http://dx.doi.org/10.1142/S0218127408021890[Crossref]
  • [20] P. Paradisi, R. Cesari, D. Contini, A. Donateo, L. Palatella, Eur. Phys. J.-Special Topics (in press)
  • [21] C. Godréche, J. M. Luck, J. Stat. Phys. 104, 489 (2001) http://dx.doi.org/10.1023/A:1010364003250[Crossref]
  • [22] P. Allegrini, G. Aquino, P. Grigolini, L. Palatella, A. Rosa, Phys. Rev. E 68, 056123 (2003) http://dx.doi.org/10.1103/PhysRevE.68.056123[Crossref]
  • [23] G. Aquino, M. Bologna, P. Grigolini, B. J. West, Phys. Rev. E 70, 036105 (2004) http://dx.doi.org/10.1103/PhysRevE.70.036105[Crossref]
  • [24] O. C. Akin, P. Paradisi, P. Grigolini, Physica A, 371, 157 (2006) http://dx.doi.org/10.1016/j.physa.2006.04.054[Crossref]
  • [25] L. Gammaitoni, P. Hanggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998) http://dx.doi.org/10.1103/RevModPhys.70.223[Crossref]
  • [26] B. Mc Namara, K. Wiesenfeld, Phys. Rev. A 39, 4854 (1989) http://dx.doi.org/10.1103/PhysRevA.39.4854[Crossref]
  • [27] O. C. Akin, P. Paradisi, P. Grigolini, J. Stat. Mech.-Theory E., 01013 (2009)
  • [28] C. Beck, E. G. D. Cohen, H. L. Swinney, Phys. Rev. E 72, 056133 (2005) http://dx.doi.org/10.1103/PhysRevE.72.056133[Crossref]

Document Type

Publication order reference


YADDA identifier

JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.