Reconstructing the state space of continuous time chaotic systems using power spectra

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 210, Issue 4-5, 1996, Pages 290-300

  Lipton, J M ^a   Dabke, K P ^a  

^a MONASH UNIVERSITY   (Australia)

Author keywords

Dimension; KS entropy; Power spectra; State space reconstruction; Time delay

Indexed keywords

ADDITIVE NOISE; CHAOTIC SYSTEMS; COMPUTATIONAL COMPLEXITY; ENTROPY; LYAPUNOV METHODS; POWER SPECTRUM; TIME DELAY;

DIMENSION; EMBEDDING DIMENSIONS; HIGH FREQUENCY HF; KOLMOGOROV-SINAI ENTROPY; LYAPUNOV EXPONENT; NUMBER OF SAMPLES; POWER-SPECTRA; STATE SPACE RECONSTRUCTION;

CONTINUOUS TIME SYSTEMS;

EID: 0005461732     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/0375-9601(95)00876-4     Document Type: Article

References (43)

1. A. Wolf et al., Physica D 16 (1985) 285.
2. H.D.I. Abarbanel et al., Rev. Mod. Phys. 65 (1993) 1331.
3. P. Grassberger and I. Procaccia, Phys. Rev. Lett. 50 (1983) 346.
4. M.B. Kennel and S. Isabelle, Phys. Rev. A 46 (1992) 3111.
5. F. Takens, in: Dynamical systems and turbulence (Warwick, 1980), Lecture notes in mathematics, eds, D.A. Rand and L.-S. Young (Springer, Berlin, 1981) pp. 366-381.
6. N.H. Packard et al., Phys. Rev. Lett. 45 (1980) 712.
7. D.S. Broomhead and G.P. King, Physica D 20 (1986) 217.
8. J.D. Farmer and J.J. Sidorowich, in: Evolution, learning, and cognition, ed. Y.S. Lee (World Scientific, Singapore, 1988) pp. 265-289.
9. G. Sugihara, B. Grenfell and R.M. May, Philos. Trans. R. Soc. B 330 (1990) 235.
10. A. Provenzale et al., Physica D 58 (1992) 31.
11. T. Sauer and J.A. Yorke, Int. J. Bifurcation Chaos 3 (1993) 737.
12. J.D. Farmer and J.J. Sidorowich, Phys. Rev. Lett. 59 (1987) 845.
13. H.D.I. Abarbanel, R. Brown and J.B. Kadtke, Phys. Lett. A 138 (1989) 401.
14. A.A. Tsonis and J.B. Eisner, Nature 359 (1992) 217.
15. D.I.T. Kaplan and L. Glass, Phys. Rev. Lett. 68 (1992) 427.
16. J. Theiler et al., Physica D 58 (1992) 77.
17. M. Casdagli, Physica D 35 (1989) 335.
18. A.A. Tsonis, Chaos: From theory to applications (Plenum, New York, 1992).
19. W. Liebert and H.G. Schuster, Phys. Lett. A 142 (1989) 107.
20. T. Mullin, The nature of chaos (Oxford Univ. Press, New York, 1993).
21. M. Casdagli, J. R. Stat. Soc. B 54 (1992) 303.
22. R.H. Abraham and C.D. Shaw, Dynamics - The geometry of behavior, Vols. 1-4 (Aerial Press, Santa Cruz, 1982).
23. J. Crutchfield et al., Phys. Lett. A 76 (1980) 1.
24. J.D. Farmer et al., Ann. NY Acad. Sci. 357 (1980) 453.
25. P.S. Linsay, Phys. Rev. Lett. 47 (1981) 1349.
26. V. Anishchenko and B. Neiman, Radiotekhnika 8 (1990) 1666.
27. A. Ushida and L. Chua, IEEE Trans. Circ. Syst. 31 (1984) 766.
28. H.G. Schuster, Deterministic chaos: An introduction (VCH, Weinheim, 1988).
29. S.N. Rasband, Chaotic dynamics of nonlinear systems (Wiley, New York, 1990).
30. D. Sigeti and W. Horsthemke, Phys. Rev. A 35 (1987) 2276.
31. D.E. Sigeti, Physica D 82 (1995) 136.
32. L.O. Chua et al., special issue on chaotic systems, in: Proc. IEEE, 1987.
33. J. Guckenheimer and P.J. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields (Springer, Berlin, 1983).
34. G. Birkhoff and G. Rotta, Ordinary differential equations (Wiley, New York, 1989).
35. U. Frisch and R. Morf, Phys. Rev. A 23 (1981) 2673.
36. C. Sparrow, The Lorenz equations: Bifurcations, chaos, and strange attractors (Springer, Berlin, 1982).
37. O.E. Rössler, Phys. Lett. A 57 (1976) 397.
38. E.N. Lorenz, Physica D 13 (1984) 90.
39. M.C. Mackey and L. Glass, Science 197 (1977) 287.
40. J.L. Kaplan and J.A. Yorke, in: Functional differential equations and approximation of fixed points, eds. H.O. Walter and H.-O. Peitgen (Springer, Berlin, 1979) pp. 204-227.
41. P. Frederickson et al., J. Diff. Eqns. 49 (1983) 185.
42. A.M. Fraser and H.L. Swinney, Phys. Rev. A 33 (1986) 1134.
43. P. Grassberger, T. Schreiber and C. Schaffrath, Int. J. Bifurcation Chaos 1 (1991) 521.