Statistical modeling and design of discrete-time chaotic processes: Advanced finite-dimensional tools and applications

Proceedings of the IEEE

Volumn 90, Issue 5, 2002, Pages 820-841

  Rovatti, Riccardo ^a,b   Mazzini, Gianluca ^a,b,c,d   Setti, Gianluca ^a,b,c,d   Giovanardi, Alessandra ^a,c  

^a IEEE   (Italy)

^b UNIVERSITY OF BOLOGNA   (Italy)

^c UNIVERSITY OF FERRARA   (Italy)

^d University of Bologna ^*  (Italy)

Author keywords

Chaotic systems; Correlations; Markov and pseudo Markov processes; Multimedia traffic; Quantized processes; Self similar processes; Statistical analysis

Indexed keywords

COMPUTER SIMULATION; CORRELATION METHODS; DISCRETE TIME CONTROL SYSTEMS; MARKOV PROCESSES; NETWORK COMPONENTS; PIECEWISE LINEAR TECHNIQUES; STATISTICAL METHODS; TELECOMMUNICATION CONTROL; TENSORS;

CHAOTIC SYSTEMS; MARKOV AND PSEUDO-MARKOV PROCESSES; MARKOV MAPS; MULTIMEDIA TRAFFIC; QUANTIZED PROCESSES; SELF SIMILAR PROCESSES;

CHAOS THEORY;

EID: 4143108076     PISSN: 00189219     EISSN: None     Source Type: Journal    
DOI: 10.1109/JPROC.2002.1015009     Document Type: Review

References (32)

1. A. Erramilli, M. Roughan, D. Veitch, and W. Willinger, "Self-similar traffic and network dynamics," Proc. IEEE, vol. 90, pp. 800-819, May 2002.
2. K. Park and W. Willinger, Self-Similar Network Traffic and Performance Evaluation. New York: Wiley, 2000.
3. B. B. Mandelbrot, "Long-run linearity, locally Gaussian processes, H-spectra and infinite variances," Int. Econom. Rev., vol. 10, pp. 82-113, 1969.
4. D. R. Cox, "Long-range dependency: A review," in Statistics: An Appraisal, H. A. David and H. T. David, Eds. Ames, IA: Iowa State Univ. Press, 1984, pp. 55-74.
5. G. Setti, G. Mazzini, R. Rovatti, and S. Callegari, "Statistical modeling and design of discrete-time chaotic processes: Basic finite-dimensional tools and applications," Proc. IEEE, vol. 90, pp. 662-690, May 2002.
6. M. Mori, "Fredholm determinant for piecewise linear transformations," Osaka J. Math., vol. 27, pp. 81-116, 1990.
7. _, "On the intermittency of a piecewise linear map (Takahashi model)," Tokyo J. Math., vol. 16, no. 2, pp. 411-428, 1993.
8. S. B. Lowen and M. C. Teich, "Fractal renewal processes generate 1/f noise," Phys. Rev. E, vol. 47, no. 2, pp. 992-1001, Feb. 1993.
9. [0, 1] noise for circuit simulation," in Proc. Int. Symp. Nonlinear Theory and its Applications, Dec. 1999, pp. 565-568.
10. J. G. Kemeny, J. L. Snell, and A. W. Knapp, Denumerable Markov Chains. Berlin, Germany: Springer-Verlag, 1976.
11. L. E. Baum and T. Petrie, "Statistical inference for probabilistic functions of finite state Markov chains," Ann. Math. Statistics, vol. 37, pp. 1554-1563, 1966.
12. J. D. Ferguson, "Hidden Markov analysis: An introduction," in Proceedings of the Symposium on the Application of Hidden Markov Models to Text and Speech, J. D. Ferguson, Ed. Princeton, NJ: Inst, for Defense Analyses, 1980.
13. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos: Springer-Verlag, 1996.
14. S. Isola, "Renewal sequences and intermittency," J. Statistical Phys., vol. 97, no. 1-2, pp. 263-280, Oct. 1999.
15. _, "Return times and mixing properties," presented at the IEEE Workshop on Nonlinear Dynamics of Electronic Systems, 2000.
16. A. L. Baranowski and W. Schwarz, "Statistical analysis and design of continuous-discrete chaos generators," IEICE Trans. Fundamental, vol. E82-A, pp. 1762-1768, 1999.
17. R. Rovatti, G. Mazzini, and G. Setti, "A tensor approach to higher-order expectations of quantized chaotic trajectories - Part I: general theory and specialization to piecewise affine Markov systems," IEEE Trans. Circuits Syst. I, vol. 47, pp. 1571-1583, Nov. 2000.
18. R. Rovatti and G. Mazzini, "Tensor function analysis of quantized chaotic piecewise-affine pseudo-Markov systems - Part I: Higher order correlations and self-similarity," IEEE Trans. Circuits Syst. 1, vol. 49, pp. 137-149, Feb. 2002.
19. _, "Tensor function analysis of quantized chaotic piece-wise-affine Pseudo-Markov systems - Part II: Higher order correlations and self-similarity," IEEE Trans. Circuits Syst. 1, vol. 49, pp. 150-162, Feb. 2002.
20. A. Giovanardi, G. Mazzini, and R. Rovatti, "Criteria to design chaotic self-similar traffic generators," IEICE Trans. Fundamentals, vol. E84-A, pp. 2155-2164, Sept. 2001.
21. G. Mazzini, R. Rovatti, and G. Setti, "Chaos-based asynchronous DS-CDMA systems," in Chaotic Electronics in Telecommunications, M. P. Kennedy, R. Rovatti, and G. Setti, Eds. Boca Raton, FL: CRC Press, 2000, ch. 3.
22. T. Kohda and A. Tsuneda, "Information sources using chaotic dynamics," in Chaotic Electronics in Telecommunications, M. P. Kennedy, R. Rovatti, and G. Setti, Eds. Boca Raton, FL: CRC Press, 2000, ch. 4.
23. T. Schimming, H. Dedieu, M. Hasler, and M. Ogorzałek, "Noise filtering in chaos-based communication," in Chaotic Electronics in Telecommunications, M. P. Kennedy, R. Rovatti, and G. Setti, Eds. Boca Raton, FL: CRC Press, 2000, ch. 8.
24. W. Schwarz, M. Götz, K. Kelber, A. Abel, T. Falk, and F. Dachselt, "Statistical analysis and design of chaotic systems," in Chaotic Electronics in Telecommunications, M. P. Kennedy, R. Rovatti, and G. Setti, Eds. Boca Raton, FL: CRC Press, 2000, ch. 9.
25. A. M. Odlyzko, "Asymptotic enumeration methods," in Handbook of Combinatorics, R. L. Graham, M. Grötschel, and L. Lovász, Eds. Cambridge, MA: MIT Press, 1995, vol. 2, pp. 1063-1229.
26. H. S. Wilf, Generatingfunctionology. San Diego, CA: Academic Press, 1994.
27. S. Wolfram, The Mathematics Book, 4th ed. Cambridge, U.K.: Cambridge Univ. Press, 1999.
28. W. E. Leland, M. S. Taqqu, W. Willinger, and D. V. Wilson, "On the self-similar nature of ethernet traffic," IEEE Trans. Networking, vol. 2, pp. 1-15, Feb. 1994.
29. W. E. Leland and D. V. Wilson, "High-time resolution measurements and analysis of LAN traffic: Implications for LAN interconnections," in Proc. INFOCOM, 1991, pp. 1360-1366.
30. A. Erramilli, P. Pruthi, and W. Willinger, "Self-similarity in high-speed network traffic measurements: Fact or artifact?," in Proc. 12th Nordic Teletraffic Seminar, 1995, pp. 299-310.
31. E. Erramilli and P. Singh, "An application of deterministic chaotic maps to model packet traffic," Queuing Syst., vol. 20, pp. 171-206, 1995.
32. S. Molnar and I. Maricza, "Source characterization in broadband networks," Proc. COST-257 Midterm Seminar, 1999.