Dynamics between order and chaos in a simple reentrant model of production dynamics

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 13, Issue 5, 2003, Pages 1343-1351

  Katzorke, I ^a   Pikovsky, A ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

Complexity; Production dynamics; Quasiperiodicity

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; QUEUEING THEORY;

REENTRANT MODELS;

CHAOS THEORY;

EID: 0043199865     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021812740300728X     Document Type: Article

References (23)

1. Badii, R. & Politi, A. [1997] Complexity. Hierarchical Structures and Scaling in Physics (Cambridge University Press, Cambridge).
2. Barlovic, R., Schadschneider, A. & Schreckenberg, M. [2001] "Random walk theory of jamming in a cellular automaton model for traffic flow," Physica A294, 525-538.
3. Beaumariage, T. & Kempf, K. [1994] Chaotic Behavior in Manufacturing Systems 2nd Annual Chaos Conf., Santa Fe; "The nature and origin of chaos in manufacturing systems," Proc. 5th IEEE/SEMI Adv. Semiconductor Manufacturing Conf. (Boston), pp. 169-174.
4. Bunimovich, L. [2001] "Dynamical systems and operation research: A basic model," Discr. Continuous Dyn. Syst. 1, 209-218.
5. Chase, C., Serrano, J. & Ramadge, P. J. [1993] "Periodicity and chaos from switched flow systems: Contrasting examples of discretely controlled continuous systems," IEEE Trans. Automat. Contr. AC-38, p. 70.
6. Chowdhury, D. & Schadschneider, A. [1999] "Self-organization of traffic jams in cities: Effects of stochastic dynamics and signal periods," Phys. Rev. E59, 1311-1314.
7. Diaz-Rivera, I., Armbruster, D. & Taylor, T. [2000] "Periodic orbits in reentrant manufacturing systems," Math. Oper. Res. 25, 708-725.
8. Ebeling, W., Steuer, R. & Titchener, M. R. [2001] "Partition based entropies of deterministic and stochastic maps," Stock. Dyn. 1, 45-61.
9. Gross, D. & Harris, C. M. [1985] Fundamentals of Queueing Theory (Wiley, NY).
10. Hanson, D., Armbruster, D. & Taylor, T. [1999] "On the stability of reentrant manufacturing systems," Proc. 31st MTNS, Padua 1998 Mathematical Theory of Networks and Systems, eds. Beghi, A., Finesso, L. & Picci, G., Il Poligrafo, Padova, Italy, pp. 937-940.
11. Helbing, D. [2001] "Die wundervolle Welt aktiver Vielteilchensysteme," Physikalische Blaetter 57, 27-33.
12. Huisinga, T., Barlovic, R., Knospe, W., Schadschneider, A. & Schreckenberg, M. [2001] "A microscopic model for packet transport in the Internet," Physica A294, 249-256.
13. Katzorke, I. & Pikovsky, A. [2000] Chaos and Complexity in Simple Models of Production Dynamics (Discrete Dynamics in Nature and Society), pp. 179-187.
14. Nelson, R. [1995] Probability, Stochastic Processes, and Queueing Theory (Springer, NY).
15. Pikovsky, A. & Feudel, U. [1994] "Correlations and spectra of strange nonchaotic attractors," J. Phys. A27, 5209-5219.
16. Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T. [1989] Numerical Recipes (Cambridge University Press, Cambridge).
17. Queffélec, M. [1987] Substitution Dynamical Systems Spectral Analysis, Springer Lecture Notes in Mathematics, Vol. 1294, Berlin.
18. Titchener, M. R. [1994] A Model for String Complexity, Salodays in Auckland Proc., pp. 101-105.
19. Titchener, M. R. [1998] A Novel Deterministic Approach to Evaluating the Entropy of Language Texts, Italic, Hsittou, Taiwan.
20. Titchener, M. R. [2001] "A measure of information," Proc. Data Compression Conf. (DCC '00), Snowbird, Utah (IEEE), pp. 353-362.
21. Schürmann, T. & Hoffmann, I. [1995] "The entropy of 'strange billiards' inside n-simplexes," J. Phys. A28, 5033-5039.
22. Zaks, M., Pikovsky, A. S. & Kurths, J. [1998] "Symbolic dynamics behind the singular continuous power spectra of continuous flow," Physica D117, 77-94.
23. Zaks, M. [2001] "Fractal Fourier spectra of Cherry flow," Physica D149, 237-247.