Identification of coupled map lattice models of stochastic spatio-temporal dynamics using wavelets

Dynamical Systems

Volumn 19, Issue 3, 2004, Pages 265-278

  Guo, L Z ^a   Billings, S A ^a  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COUPLED MAP LATTICES (CML); LEAST SQUARE ALGORITHMS; NONLINEAR FUNCTIONALS; SPATIO-TEMPORAL DYNAMICS;

IDENTIFICATION (CONTROL SYSTEMS); LEAST SQUARES APPROXIMATIONS; MAPS; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS; PERTURBATION TECHNIQUES; PROBABILITY DENSITY FUNCTION;

STOCHASTIC CONTROL SYSTEMS;

EID: 4444333375     PISSN: 14689367     EISSN: None     Source Type: Journal    
DOI: 10.1080/14689360410001730773     Document Type: Article

References (26)

1. Adamatzky, A., 2003, On patterns in affective media. International Journal of Modern Physics C, 14(5), 673-687.
2. Bertram, M., Beta, C., Pollmann, M., Mikhailov, A. S., Rotermund, H. H., and Ertl, G., 2003, Pattern formation on the edge of chaos: experiments with CO oxidation on a Pt(110) surface under global delayed feedback. Physical. Review E, 67(3), 036208.
3. Billings, S. A., Guo, L. Z., and Wei, H. L., 2003a, Identification of spatio-temporal systems using multi-resolution wavelet models (submitted for publication).
4. Billings, S. A., Wei, H. L., Mei, S. S., and Guo, L. Z., 2003b, Identification of coupled map lattice models for spatio-temporal patterns using wavelets (submitted for publication).
5. Blanc-Talon, J., 1999 Effective computation of 2D coupled map lattices. Complexity International, 6.
6. Chen, S., Billings, S. A., and Luo, W., 1989, Orthogonal least squares methods and their application to non-linear system identification.comma. International Journal of Control, 50(5), 1873-1896.
7. Chui, C. K., and Wang, J. Z., 1991, A general framework of compactly supported splines and wavelets. Journal of Approximation Theroy, 71, 263-304.
8. Coca, D., and Billings, S. A., 2001, Identification of coupled map lattice models of complex spatio-temporal patterns. Physics Letters, A287, 65-73.
9. Coca, D., and Billings, S. A., 2003, Analysis and reconstruction of stochastic coupled map lattice models. Physics Letters, A315, 61-75.
10. DeVore, R. A., Jawerth, B., and Popov, V., 1992, Compression of wavelet decompositions. American Journal of Mathematics, 114, 737-785.
11. Goldman, D. I., Shattuck, M. D., Sung, J. M., Swift, J. B., and Swinney, H. L., 2003, Lattice dynamics and melting of a nonequilibrium pattern. Physical Review Letters, 90(10), 104302.
12. Grabec, I. and Mandelj, S., 1997, Continuation of chaotic fields by RBFNN. In Biological and Artificial Computation: From Neuroscience to Technology: Proc., Lecture Notes in Computer Science, Vol. 1240, edited by J. Mira et al. (Berlin: Springer-Verlag), pp. 597-606.
13. Gradisek, J., Siegert, S., Friedrich, R., and Grabec, I., 2000, Analysis of time series from stochastic processes. Physical Review E, 62(3), 3146-3155.
14. Guo, L. Z., Mei, S. S., and Billings, S. A., 2002, Neighbourhood detection and identification of spatio-temporal dynamical systems using a coarse-to-fine approach (submitted for publication).
15. Infeld, E., and Rowlands, G., 2000, Nonlinear Waves, Solitons, and Chaos, 2nd edn (Cambridge: Cambridge University Press).
16. Kaneko, K. (editor), 1993, Coupled Map Lattices: Theory and Experiment (Singapore: World Scientific).
17. Köhler, P., Reinhard, K., and Huth, A., 2002, Simulating anthropogenic impacts to bird communities in tropical rain forests. Biological Conservation, 108, 35-47.
18. Losson, J., and Mackey, M., 1995, Evolution of probability densities in stochastic coupled map lattices. Physical Review E, 52(2), 1403-1420.
19. Mandelj, S., Grabec, I., and Govekar, E., 2001, Statistical approach to modeling of spatiotemporal dynamics. International Journal of Bifurcation and Chaos, 11(11), 2731-2738.
20. Marcos-Nikolaus, P., Martin-Gonzalez, J. M., and Sole, R. V., 2002, Spatial forcasting: detecting determinism from single snapshots, International Journal of Bifurcation and Chaos, 12,(2), 369-376.
21. Parlitz, U., and Merkwirth, C., 2000, Prediction of spatiotemporal time series based on reconstructed local states. Physical Review Letters, 84(9), 2820-2823.
22. Sóle, R. V., Valls, J., and Bascompte, J., 1992, Spiral waves, chaos and multiple attactors in lattice models of interacting populations. Physics Letters, A166(2), 123-128.
23. Tabor, M., 1989, Chaos and Integrability in Nonlinear Dynamics: An Introduction. (New York: Wiley).
24. Tabuchi, E., Yakawa, T., Mallick, H., Inubushi, T., Kondoh, T., Ono, T., and Torii, K., 2002, Spatio-temporal dynamics of brain activated regions during drinking behaviour in rats. Brain Research, 951, 270-279.
25. Takasaki, K., 2004, Many faces of solitons. Available at: http://www.math.h.kyoto-u.ac.jp/takasaki/ soliton-lab/gallery/solitons/sg-e.html
26. Yanagita, T., and Kaneko, K., 1997, Modeling and characterisation of cloud dynamics. Physical Review Letters, 78(22), 4297-4300.