Deterministic point processes generated by threshold crossings: Dynamics reconstruction and chaos control

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 55, Issue 3, 1997, Pages 2397-2402

  Ding, Mingzhou ^a   Yang, Weiming ^a  

^a Center for Complex Systems   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000532986     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.2397     Document Type: Article

References (31)

1. See, for example, D.R. Cox and V. Isham, Point Processes (Chapman and Hall, New York, 1980); D.J. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes (Springer-Verlag, New York, 1988).
2. H. Preissl, A. Aertsen, and G. Palm, in Parallel Processing in Neural Systems and Computers, edited by R. Eckmiller, G. Hartmann, and G. Hauske (North-Holland, Amsterdam, 1990).
3. E R. Kandel, J H. Schwartz, and T M. Jessel, Principles of Neural Science (Appleton and Lange, Norwalk, 1991).
4. T. Sauer, Phys. Rev. Lett.72, 3811 (1994).
5. For studies concerning other deterministic aspects such as predictability in point processes, see A. Longtin, Int. J. Bif. Chaos3, 651 (1993);
6. A. Longtin, A. Bulsara and F. Moss, Phys. Rev. Lett.67, 656 (1991).
7. A. Garfinkel, M L. Spano, W L. Ditto and J N. Weiss, Science257, 1230 (1992);
8. S J. Schiff, K. Jerger, D H. Duong, T. Chang, M L. Spano and W L. Ditto, Nature (London)370, 615 (1994).
9. J.-P. Eckmann and D. Ruelle, Rev. Mod. Phys.57, 617 (1985).
10. P. Grassberger and I. Procaccia, Phys. Rev. Lett.50, 346 (1983);
11. P. Grassberger and I. Procaccia, Physica D9, 189 (1983).
12. R. Castro and T. Sauer (unpublished).
13. For a nonautonomous system one can make it into an autonomous one by introducing time as an additional variable.
14. F. Takens, in Dynamical Systems and Turbulence, edited by D. Rand and L.S. Young (Springer-Verlag, Berlin, 1981), p. 366;
15. T. Sauer, J A. Yorke and M. Casdagli, J. Stat. Phys.65, 579 (1991).
16. M. Ding, C. Grebogi, E. Ott, T. Sauer and J A. Yorke, Phys. Rev. Lett.70, 3872 (1993);
17. M. Ding, C. Grebogi, E. Ott, T. Sauer and J A. Yorke, Physica D69, 404 (1993).
18. K J. Falconer, The Geometry of Fractal Sets (Cambridge University Press, Cambridge, 1985).
19. E. Ott, C. Grebogi and J A. Yorke, Phys. Rev. Lett.64, 1196 (1990).
20. For reviews, see T A. Shinbrot, C. Grebogi, E. Ott and J A. Yorke, Nature (London)363, 411 (1993);
21. W L. Ditto and L M. Pecora, Sci. Am.269, (8), 78 (1993);
22. G. Chen and X. Dong, Int. J. Bif. Chaos3, 1363 (1993);
23. E.R. Hunt and G. Johnson, IEEE Spectrum, 30 (11), 32 (1993);
24. R. Roy, Z. Gills, and K S. Thornburg, Opt. Photon. News5, (5), 8 (1994);
25. E. Ott and M L. Spano, Phys. Today48, (5), 34 (1995).
26. M. Ding, W. Yang, V. In, W L. Ditto, M L. Spano and B. Gluckman, Phys. Rev. E53, 4334 (1996).
27. U. Dressler and G. Nitsche, Phys. Rev. Lett.68, 1 (1992);
28. P. So and E. Ott, Phys. Rev. E51, 2955 (1995);
29. V. Petrov, E. Mihaliuk, S K. Scott and K. Showalter, Phys. Rev. Eibid. 51, 3988 (1995).
30. E N. Lorenz, J. Atmos. Sci.20, 130 (1963).
31. C. Sparrow, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors (Springer-Verlag, New York, 1982).