Detecting switch dynamics in chaotic time-waveform using a parametrized family of nonlinear predictors

Physica D: Nonlinear Phenomena

Volumn 135, Issue 1-2, 2000, Pages 63-78

  Tokuda, Isao ^a   Tokunaga, Ryuji ^b   Matsumoto, Takashi ^c  

^a MURORAN INSTITUTE OF TECHNOLOGY   (Japan)

^b UNIVERSITY OF TSUKUBA   (Japan)

^c WASEDA UNIVERSITY   (Japan)

Author keywords

47.52.+j; Bifurcation; Chaos; Chaotic time waveform; Non stationarity; Parametrized family of nonlinear predictors; Switch dynamics

Indexed keywords

EID: 0039742048     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00124-4     Document Type: Article

References (40)

1. Abarbanel H.D.I., Brown R., Sidorowich J.J., Tsimring L.S. The analysis of observed chaotic data in physical systems. Rev. Mod. Phys. 65(4):1993;1331.
2. Grassberger P., Procassia I. Measuring the strangeness of strange attractors. Physica D. 9:1983;189.
3. Wolf A., Swift J.B., Swinney H.L., Vastano J.A. Determining Lyapunov exponents from a time series. Physica D. 16:1985;285.
4. Sano M., Sawada Y. Measurement of the Lyapunov spectrum from chaotic time series. Phys. Rev. Lett. 55:1985;1082.
5. Eckmann J.P., Kamphorst S.O., Ruelle D., Ciliberto S. Lyapunov exponents from a time series. Phys. Rev. A. 34(6):1986;4971.
6. Fraser A.M. Information and entropy in strange attractors. IEEE Trans. Info. Theor. 35:1989;245.
7. Crutchfield J.P., McNamara B.S. Equations of motion from a data series. Complex Systems. 1:1987;417.
8. Farmer J.D., Sidorowich J.J. Predicting chaotic time series. Phys. Rev. Lett. 59:1987;845.
9. A. Lapedes, R. Farber, Nonlinear signal processing using neural networks, Tech. Rep. Los Alamos National Lab. (1987) LA-UR-87-2662.
10. Casdagli M. Nonlinear prediction of chaotic time series. Physica D. 35:1989;335.
11. Sugihara G., May R.M. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature. 344:1990;734.
12. Cross M.C., Hohenberg P.C. Pattern formation outside of equilibrium. Rev. Mod. Phys. 65(3):1993;851.
13. Cuomo K.M., Oppenheim A.V. Circuit implementation of synchronized chaos with applications to communications. Phys. Rev. Lett. 71(1):1993;65.
14. Dedieu H., Kennedy M.P., Hasler M. Chaos shift keying. IEEE Trans. CAS. 40(10):1993;634.
15. Pérez G., Cerdeira H.A. Extracting messages masked by chaos. Phys. Rev. Lett. 74(11):1995;1970.
16. Pecora L.M., Carroll T.L. Synchronization in chaotic systems. Phys. Rev. Lett. 64(8):1990;821.
17. Carroll T.L., Pecora L.M. Synchronizating chaotic circuits. IEEE Trans. CAS. 38(4):1991;453.
18. Isliker H., Kurths J. A test for stationarity. Int. J. Bifurcation and Chaos. 3(6):1993;1573.
19. Manuca R., Savit R. Stationarity and nonstationarity in time series analysis. Physica D. 99:1996;134.
20. Casdagli M.C. Recurrence plots revisited. Physica D. 108:1997;12.
21. Schreiber T. Detecting and analyzing nonstationarity in a time series using nonlinear cross predictions. Phys. Rev. Lett. 78(5):1997;843.
22. Schreiber T., Schmitz A. Classification of time series data with nonlinear similarity measures. Phys. Rev. Lett. 79(8):1997;1475.
23. Kennel M.B. Statistical test for dynamical nonstationarity in observed time series data. Phys. Rev. E. 56(1):1997;316.
24. Witt A., Kurths J., Pikovsky A Testing stationarity in time series. Phys. Rev. E. 58(2):1998;1800.
25. Tokunaga R., Kajiwara S., Matsumoto T. Reconstructing bifurcation diagrams only from time-waveforms. Physica D. 79:1994;348.
26. Tokuda I., Kajiwara S., Tokunaga R., Matsumoto T. Recognizing chaotic time-waveforms in terms of a parametrized family of nonlinear predictors. Physica D. 95:1996;380.
27. F. Takens, Detecting strange attractors in turbulence, in: Lecture Notes in Mathematics, vol. 898 Springer, Berlin, 1981, p. 366.
28. T. Sauer, J.A. York, M. Casdagli, Embedology, J. Stat. Phys. 65(3) (1991) 579.
29. D.E. Rumelhart, J.L. McClelland, and the PDP Research Group, Parallel Distributed Processing, MIT Press, Cambridge, 1986.
30. Williams R.J., Zipser D. A Learning algorithm for continually running fully recurrent neural networks. Neur. Comput. 1:1989;270.
31. T.W. Anderson, An Introduction to Multivariate Statistical Analysis, Wiley, New York, 1958.
32. Broomhead D.S., King G.P. Extracting qualitative dynamics from experimental data. Physica D. 20:1986;217.
33. Albano A.M., Muench J., Schwartz C., Mees A.I., Rapp P.E. Singular-value decomposition and the Grassberger-Procaccia algorithm. Phys. Rev. A. 38(6):1988;3017.
34. Mees A.I., Rapp P.E., Jennings L.S. Singular-value decomposition and embedding dimension. Phys. Rev. A. 36(1):1987;341.
35. D.G. Luenberger, Linear and Nonlinear Programming, Addison-Wesley, Reading, MA, 1973.
36. Y. Linde, A. Buzo, R. Gray, An algorithm for vector quantizer design, IEEE. Trans. Comm. COM-28-1 (1980) 84.
37. Lorenz E.N. Deterministic nonperiodic flow. J. Atmos. Sci. 20:1963;901.
38. Rössler O.E. Continuous chaos. Ann. N.Y. Acad. Sci. 31:1979;376.
39. Mackey M.C., Glass L. Oscillation and chaos in physiological control systems. Science. 197:1977;287.
40. Kaneko K. Pattern dynamics in spatiotemporal chaos. Physica D. 34:1989;1.