Introduction to archetypal analysis of spatio-temporal dynamics

Physica D: Nonlinear Phenomena

Volumn 96, Issue 1-4, 1996, Pages 110-131

  Stone, Emily ^a   Cutler, Adele ^a  

^a UTAH STATE UNIVERSITY   (United States)

Author keywords

Archetypal analysis; Archetypes; Dynamical systems; Intermittency; Principal components

Indexed keywords

EID: 0000456941     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/0167-2789(96)00016-4     Document Type: Article

References (19)

1. D. Armbruster, J Guckenheimer and P. Holmes, Kuramoto-Sivashinsky dynamics on the center-unstable manifold, SIAM J. Appl. Math. 49 (1989) 676.
2. D. Armbruster, R. Heiland and E. Kostelich, KLTOOL: A tool to analyze spatio-temporal complexity, Chaos 4(2) (1994) 421.
3. N. Aubry, P. Holmes, J.L. Lumley and E. Stone, The dynamics of coherent structures in the wall region of a turbulent boundary layer, J. Fluid Mech. 192 (1988) 115.
4. N. Aubry, R. Guyonnet and R. Lima, Spatio-temporal analysis of complex signals: Theory and applications, J. Statist. Phys. 63 (1991) 683.
5. G. Berkooz, P. Holmes and J.L. Lumley, The proper orthogonal decomposition in the analysis of turbulent flow, Ann. Rev. Fluid Mech. 25 (1993) 115.
6. A. Cutler and L. Breiman, Archetypal analysis, Technometrics 36 (1994) 338.
7. M. el-Hamdi, M. Gorman and K.A. Robbins, Deterministic chaos in laminar premixed flames: Experimental classification of chaotic dynamics, Combustion Science and Technology, to appear.
8. M. Gorman, M. el-Hamdi and K.A. Robbins, Spatio-temporal chaotic dynamics of pre-mixed flames, Proc. of the First Experimental Chaos Conf., eds. S. Vohra, M. Spano, M. Schlesinger, L. Pecora and W. Ditto (World Scientific, Singapore, 1992) pp. 103.
9. J.M. Hyman, B. Nicolaenko and S. Zaleski, Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces, Physica D 23 (1986) 265.
10. I.G. Kevrikidis, B. Nicolaenko and C. Scovel, Back in the saddle again: A computer assisted study of the Kuramoto-Sivashinsky equation, SIAM J. Appl. Math. 50 (1990) 760.
11. M. Kirby and D. Armbruster, Reconstructing phase-space from PDE simulations, ZAMP 43 (1992) 999.
12. M. Kirby and L. Sirovich, Application of the Karhunen-Loève procedure for the characterization of human faces, IEEE Trans. PAMI 12 (1990) 103.
13. J.L. Lumley, The structure of inhomogeneous turbulent flows, in: Atmospheric Turbulence and Radio Wave Propagation, eds. A.M. Yaglom and V.I. Tatarski (Nauka, Moscow, 1967) 166.
14. L. Sirovich, Turbulence and the dynamics of coherent structures Parts I-III, Quart. Appl. Math. XLV (3) (1987) 561.
15. L. Sirovich and J. Rodriguez, Coherent structures and chaos: A model problem, Phys. Lett. A 120 (1987) 211.
16. L. Sirovich and M. Kirby, A low-dimensional procedure for the characterization of human faces, J. Opt. Soc. Amer. A 4(3) (1987) 519.
17. G.I. Sivashinsky, Nonlinear analysis of hydrodynamic stability of laminar flames - Derivation of basic equations, Acta Astr. 4 (1977) 1177.
18. E. Stone and A. Cutler, Archetypal analysis of intermittent dynamics, Physica D 90 (1996) 209-224.
19. Watanabe, The Karhunen Loève expansion and factor analysis, The Proc. of the 4th Prague Conf. on Information Theory and Statistical Decision Functions (1965).