Testing for Unstable Periodic Orbits to Characterize Spatiotemporal Dynamics

Chaos, Solitons and Fractals

Volumn 9, Issue 8, 1998, Pages 1429-1438

  Zoller G ^a   Engbert, R ^a   Hainzl, S ^a   Kurths, J ^a  

^a UNIVERSITY OF POTSDAM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DATA REDUCTION; DYNAMICS; TIME SERIES ANALYSIS;

SPATIOTEMPORAL DYNAMICS; UNSTABLE PERIODIC ORBITS;

CHAOS THEORY;

EID: 0032131445     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. Grassberger, P., Schreiber, T. and Schaffrath, C., Nonlinear time sequence analysis. Intern. J. Bif. Chaos, 1991, 1, 521-547; Kantz. H. and Schreiber, T. Nonlinear Time Series Analysis. Cambridge University Press, Cambridge, 1997.
2. Grassberger, P., Schreiber, T. and Schaffrath, C., Nonlinear time sequence analysis. Intern. J. Bif. Chaos, 1991, 1, 521-547; Kantz. H. and Schreiber, T. Nonlinear Time Series Analysis. Cambridge University Press, Cambridge, 1997.
3. Ott, E. T. Sauer and Yorke, J. A., eds, Coping with Chaos. John Wiley & Sons, New York, 1994.
4. Hassel, M. P., Comins, H. and May, R. M., Species coexistence and self-organizing spatial dynamics. Nature, 1994, 370, 290-292; Nowak, M. A. and May, R. M., Evolutionary games and spatial chaos, Nature, 1992, 359, 826-829.
5. Hassel, M. P., Comins, H. and May, R. M., Species coexistence and self-organizing spatial dynamics. Nature, 1994, 370, 290-292; Nowak, M. A. and May, R. M., Evolutionary games and spatial chaos, Nature, 1992, 359, 826-829.
6. Hämäläinen, M., Hari, R., Illmoniemi, R. J., Knuutila, J. and Lounasmaa, O. V., Magnetoencephalography -theory, instrumentation, and applications to noninvasive studies of the working human brain. Rev. Mod. Phys., 1993, 65, 413-498.
7. Rossi, G., Fractal analysis as a tool to detect seismic cycle phases. In Fractals and Dynamic Systems in Geoscience, ed. J. H. Kruhl. Springer-Verlag, Berlin, 1994, pp. 169-179.
8. Chui, C. K., An Introduction to Wavelets. Academic Press, Boston, 1992.
9. Uhl, C., Friedrich, R. and Haken, H., Analysis of spatio-temporal signals of complex systems. Phys. Rev. E, 1992, 51, 3890-3900.
10. Rand, D. A., Measuring and characterizing spatial patterns, dynamics and chaos in spatially extended dynamical systems and ecologies. Phil. Trans. R. Soc. Lond. A, 1994, 348, 497-514.
11. Rand, D. A. and Wilson, H. B., Using spatio-temporal chaos and intermediate-scale determinism to quantify spatially extended ecosystems. Proc. R. Soc. Lond. B, 1995, 259, 111-117.
12. Haken, H., Synergetics. Springer-Verlag, Berlin, 1988.
13. Pei, X. and Moss, F., Characterization of low-dimensional dynamics in the crayfish caudal photoreceptor. Nature, 1996, 379, 618-620.
14. Schiff, S. J., Jerger, K., Duong, D. H., Chang, T., Spano, M. L. and Ditto, W. L., Controlling chaos in the brain. Nature, 1994, 370, 615-620.
15. So, P., Ott, E., Schiff, S. J., Kaplan, D. T., Sauer, T. and Grebogi, C., Detecting unstable periodic orbits in chaotic experimental data. Phys. Rev. Lett., 1996, 76, 4705-4708.
16. Schmelcher, P. and Diakonos, F. K., Detecting unstable periodic orbits of chaotic dynamical system. Phys. Rev. Lett., 1997, 78, 4733-4735.
17. Theiler, J., Eubank, S., Longtin, A., Galdrikian, B. and Farmer, J. D., Testing for nonlinearity in time series: the method of surrogate data. Physica D 58, 77-94 (1992); Theiler, J., Galdrikian, B., Longtin, A., Eubank, S. and Farmer, J.D., Using surrogate data to detect nonlinearity in time series. In Nonlinear Modeling and Forecasting. SFI Studies in the Sciences of Complexity, eds M. Casdagli and S. Eubank, Proc. Vol. XII, Addison Wesley, New York, 1992, pp. 163-188.
18. Theiler, J., Eubank, S., Longtin, A., Galdrikian, B. and Farmer, J. D., Testing for nonlinearity in time series: the method of surrogate data. Physica D 58, 77-94 (1992); Theiler, J., Galdrikian, B., Longtin, A., Eubank, S. and Farmer, J.D., Using surrogate data to detect nonlinearity in time series. In Nonlinear Modeling and Forecasting. SFI Studies in the Sciences of Complexity, eds M. Casdagli and S. Eubank, Proc. Vol. XII, Addison Wesley, New York, 1992, pp. 163-188.
19. Kaneko, K., ed., Theory and Applications of Coupled Map Lattices. Wiley, Chichester, 1993.
20. Ott, E., Chaos in Dynamical Systems. Cambridge University Press, Cambridge, 1993.
21. Rudzick, O., Pikovsky, A., Scheffczyk, C. and Kurths, J., Dynamics of chaos-order interface in coupled map lattices. Physica D, 1997, 103, 330-347.
22. Turcotte, D. L., Fractals and Chaos in Geology and Geophysics. Cambridge University Press, Cambridge, 2nd edn, 1997.
23. Gutenberg, B. and Richter, C. F., Earthquake magnitude, intensity, energy and acceleration. Bull. Seismol. Soc. Am., 1954, 46, 105-145.
24. Frohlich, C. and Davis, S. D., Teleseismic b-values; or, much ado 1.0. J. Geophys. Res., 1993, 98, 631-644.
25. Martirosyan, A. H., Armenia Earthquake Catalogue, unpublished. GeoForschungsZentrum Potsdam (1997).
26. Zschau, J., Welle, W., Ates, A. and Berkhemer, H., SEISMOLAP: A new approach to prediction. In Earthquake Prediction: State-of-the-Art. Council of Europe, EMSC, 1991, pp. 585-606.