Compression and diffusion: A joint approach to detect complexity

Chaos, Solitons and Fractals

Volumn 15, Issue 3, 2003, Pages 517-535

  Allegrini, P ^a,b   Benci, V ^c   Grigolini, P ^b,c,d   Hamilton, P ^e   Ignaccolo, M ^b   Menconi, G ^c   Palatella, L ^c   Raffaelli, G ^f   Scafetta, N ^b   Virgilio, M ^c   Yang, J ^b  

^a CNR Consiglio Nazionale delle Ricerche   (Italy)

^b UNIVERSITY OF NORTH TEXAS   (United States)

^c UNIVERSITY OF PISA   (Italy)

^d CNR Consiglio Nazionale delle Ricerche   (Italy)

^e TEXAS WOMAN'S UNIVERSITY   (United States)

^f SISSA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BROWNIAN MOVEMENT; DIFFUSION; DYNAMICS; MATHEMATICAL TECHNIQUES; NUMERICAL ANALYSIS; TIME SERIES ANALYSIS;

DYNAMICAL SYSTEMS;

ENTROPY;

EID: 18544389239     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(02)00136-4     Document Type: Article

References (39)

1. Allegrini P., Barbi M., Grigolini P., West B.J. Dynamical model for DNA sequences. Phys. Rev. E. 52:1995;5281-5296.
2. Allegrini P., Grigolini P., Hamilton P., Palatella L., Raffaelli G., Virgilio M. Facing non-stationary conditions with a new indicator of entropy increase: the cassandra algorithm. Novak M.M. Emergent Nature. 2001;183-184 World Scientific, Singapore. arXiv:cond-mat/0111246.
3. Allegrini P., Grigolini P., West B.J. Dynamical approach to levy processes. Phys. Rev. E. 54:1996;4760-4767.
4. Annunziato M., Grigolini P. Stochastic versus dynamic approach to levy statistics in the presence of an external perturbation. Phys. Lett. A. 269:2000;31-39.
5. Aquino G., Grigolini P., Scafetta N. Sporadic randomness, maxwell's demon and the poincare recurrence times. Chaos, Solitons and Fractals. 12:2001;2023-2038.
6. Argenti F., Benci V., Cerrai P., Cordelli A., Galatolo S., Menconi G. Information and dynamical systems: a concrete measurement on sporadic dynamics. Chaos, Solitons and Fractals. 13(3):2002;461-469.
7. Baranger M., Latora V., Rapisarda A. Time evolution of thermodynamic entropy for conservative and dissipative chaotic maps. Chaos, Solitons and Fractals. 13(3):2002;471-478.
8. Bar-Yam Y. Dynamics of Complex Systems. 1997;Addison-Wesley, Reading, MA.
9. Beck C., Schlögl F. Thermodynamics of Chaotic Systems: An Introduction. 1993;Cambridge Nonlinear Science, Cambridge.
10. Bedeaux D., Lakatos Lindenberg L., Shuler K.E. On the relation between master equation and random walks and their solutions. J. Math. Phys. 12:1971;2116.
11. Benci V, Bonanno C, Galatolo S, Menconi G, Ponchio F. Information, complexity and entropy: a new approach to theory and measurements methods, in press. Available from http://arXiv.org/abs/math.DS/0107067.
12. Bologna M., Grigolini P., Karagiorgis M., Rosa A. Trajectory versus probability density entropy. Phys. Rev. E. 64(1-9):2001;016223.
13. Bonanno C. The Manneville map: topological, metric and algorithmic entropy, 2001. Available from http://arXiv.org/abs/math.DS/0107195.
14. Bonanno C, Menconi G. Computational information for the logistic map at the chaos threshold, Discrete Contin. Dyn. Syst. B, in press. arXiv E-print no. nlin.CD/0102034.
15. Brudno A.A. Entropy and the complexity of a dynamical system. Trans. Moscow Math. Soc. 2:1983;127-151.
16. Buiatti M., Grigolini P., Palatella L. A nonextensive approach to the entropy of symbolic sequences. Physica A. 268:1999;214-224.
17. Bologna M, Campisi M, Grigolini P. Dynamic versus thermodynamic approach to non-equilibrium. Physica A 2002;305:89-92, arXiv: cond-mat/0108361.
18. Chaitin G.J. Information, randomness and incompleteness. Papers on algorithmic information theory. 1987;World Scientific, Singapore.
19. Dorfman J.R. An introduction to chaos in nonequilibrium statistical mechanics. Cambridge Lecture Notes in Physics. 1999;Cambridge University Press, Cambridge.
20. Fronzoni L., Grigolini P., Montangero S. Nonextensive thermodynamics and stationary processes of localization. Chaos, Solitons and Fractals. 11(14):2000;2361-2369.
21. Fronzoni L., Montangero S., Grigolini P. The complexity of the logistic map at the chaos threshold. Phys. Lett. A. 285(1-2):2001;81-87.
22. Galatolo S. Orbit complexity and data compression. Discrete Contin. Dyn. Syst. 7:2001;477-486.
23. Galatolo S. Orbit complexity by computable structures. Nonlinearity. 13:2000;1531-1546.
24. Galatolo S. Orbit complexity, initial data sensitivity and weakly chaotic dynamical systems, 2001. arXiv E-print no. math.DS/0102187.
25. Galatolo S. Pointwise information entropy for metric spaces. Nonlinearity. 12:1999;1289-1298.
26. Gaspard P., Wang X.J. Sporadicity: between periodic and chaotic dynamical behavior. Proc. Natl. Acad. Sci. USA. 85:1988;4591-4595.
27. Geisel T., Thomae S. Anomalous diffusion in intermittent chaotic systems. Phys. Rev. Lett. 52:1984;1936.
28. Grigolini P., Palatella L., Raffaelli G. Asymmetric anomalous diffusion: an efficient way to detect memory in time series. Fractals. 9:2001;193-208.
29. Grigolini P, Leddon D, Scafetta N. Diffusion entropy and waiting time statistics of hard X-ray solar flares. Phys Rev E 2002;65:046203, 1-3. cond-mat/0108229.
30. Ignaccolo M., Grigolini P., Rosa A. Sporadic randomness: the transition from the stationary to the nonstationary condition. Phys. Rev. E. 64:2001;026210.
31. Mandelbrot B.B. Fractal Geometry of Nature. 1988;W.H. Freeman, San Francisco, CA.
32. Manneville P. Intermittency, self similarity and spectrum in dissipative dynamical systems. J. Phys. 41:1980;1235-1243.
33. Peng C.-K., Buldyrev S.V., Havlin S., Simons M., Stanley H.E., Goldberger A.L. Mosaic organisation of DNA nucleotides. Phys. Rev. E. 49:1994;1685.
34. Peng C.-K., Havlin S., Stanley H.E., Goldberger A.L. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos. 5:1995;82-87.
35. Scafetta N., Hamilton P., Grigolini P. The thermodynamics of social processes: the teen birth phenomenon. Fractals. 9:2001;193-208.
36. Scafetta N, Latora V, Grigolini P. Levy statistics in coding and noncoding DNA, 2001. cond-mat/0105041.
37. Sokolov I.M. Thermodynamics and fractional Fokker-Planck equations. Phys. Rev. 63:2001;0566111-1-0566111-8.
38. Sokolov I.M., Klafter J., Blumen A. Do strange kinetics imply unusual thermodynamics? Phys. Rev. E. 64:2001;021107-1-021107-4.
39. Tsallis C. Entropic nonextensivity: a possible measure of complexity. Chaos, Solitons and Fractals. 13:2002;371-391.