Scaling and interleaving of subsystem Lapunov exponents for spatio-temporal systems

Chaos

Volumn 9, Issue 2, 1999, Pages 466-482

  Carretero Gonzalez R ^a   ORstavik S ^a   Huke, J ^b   Broomhead, D S ^b   Stark, J ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040318527     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166420     Document Type: Article

References (43)

1. J. L. Kaplan and J. A. Yorke, Chaotic behaviour of multidimensional difference equations, Lecture Notes in Mathematics (Springer, New York, 1979) Vol. 730, pp. 204-227.
2. H. G. Schuster, Deterministic chaos (VCH Verlagsgesellschaft, Weinheim, 1988), 2nd ed.
3. J.-P. Eckmann and D. Ruelle, "Ergodic theory of chaos and strange attractors," Rev. Mod. Phys. 57(3), 617-656 (1985).
4. P. Grassberger, "Information content and predictability of lumped and distributed dynamical systems," Phys. Scr. 40, 346-353 (1989).
5. G. P. Puccioni, A. Torcini, A. Politi, and G. D'Alessandro, "Fractal dimension of spatially extended systems," Physica D 53, 85-101 (1991).
6. M. Bauer, H. Heng, and W. Martienssen, "Characterization of spatiotemporal chaos from time series," Phys. Rev. Lett. 71(4), 521-524 (1993).
7. K. Geist, U. Parlitz, and W. Lauterborn, "Comparison of different methods for computing Lyapunov exponents," Prog. Theor. Phys. 83(5), 875-893 (1990).
8. H. F. von Bremen, F. E. Udwadia, and W. Proskurowski, "An efficient QR based method for the computation of Lyapunov exponents," Physica D 101, 1-16 (1997).
9. D. Ruelle, "Large volume limit distribution of characteristic exponents in turbulence," Commun. Math. Phys. 87, 287-302 (1982).
10. Ya. G. Sinai, "A remark concerning the thermodynamic limit of the Lyapunov spectrum," Int. J. Bifurcation Chaos Appl. Sci. Eng. 6(6), 1137-1142 (1996).
11. Ya. G. Sinai and N. I. Chernov, "Entropy of a gas of hard spheres with respect to the group of space-time shifts," Proc. of Petrovski Seminar 8, 218-238 (1982).
12. M. Bauer and W. Martienssen, "Lyapunov exponents and dimensions of chaotic neural networks," J. Phys. A 24, 4557-4566 (1991).
13. K. Kaneko, "Towards thermodynamics of spatiotemporal chaos," Prog. Theor. Phys. Suppl. 99, 263-287 (1989).
14. N. Parekh, V. R. Kumar, and B. D. Kulkarni, "Analysis and characterization of complex spatio-temporal patterns in nonlinear reaction-diffusion systems," Physica A 224, 369-381 (1996).
15. N. Parekh, V. R. Kumar, and B. D. Kulkarni, "Control of spatiotemporal chaos: a study with an autocatalytic reaction-diffusion systems," Pramana, J. Phys. 48(1), 303-323 (1997).
16. D. Ruelle, "Five turbulent problems," Physica D 7, 40-44 (1983).
17. P. Manneville, "Liapounov exponents for the Kuramoto-Sivashinsky model," in Macroscopic modeling of turbulent flows, Lecture Notes in Physics (Springer-Verlag, Berlin, 1985) Vol. 230, pp. 319-326.
18. S. Ørstavik, R. Carretero-González, J. Huke, D. S. Broomhead, and J. Stark, "Interleaving and estimation of intensive measures in spatio-temporal systems from time-series," (in preparation).
19. B. R. Parlett, The symmetric eigenvalue problem (Prentice-Hall, Englewood Cliffs, NJ, 1980).
20. K. Kaneko, "Transition from torus to chaos accompanied by frequency lockings with symmetry breaking," Prog. Theor. Phys. 69(5), 1427 (1983).
21. K. Kaneko, "Period-doubling of kink-antikink patterns, quasiperiodicity in anti-ferro-like structures and spatial intermittency in coupled logistic lattice," Prog. Theor. Phys. 72(3), 480-486 (1984).
22. P. M. Gade and R. E. Amritkar, "Spatially periodic orbits in coupled map lattices," Phys. Rev. E 47(1), 143-153 (1993).
23. Q. Zhilin, H. Gang, M. Benkun, and T. Gang, "Spatiotemporally periodic patterns in symmetrically coupled map lattices," Phys. Rev. E 50(1), 163-170 (1994).
24. R. Carretero-González, D. K. Arrowsmith, and F. Vivaldi, "Mode-locking in coupled map lattices," Physica D 103, 381-403 (1997).
25. R. Kapral, R. Livi, G.-L. Oppo, and A. Politi, "Dynamics of complex interfaces," Phys. Rev. E 49(3), 2009-2022 (1994).
26. D. Keeler and J. D. Farmer, "Robust space-time intermittency and 1/f noise," Physica D 23, 413-435 (1986).
27. C. Beck, "Chaotic cascade model for turbulent velocity distribution," Phys. Rev. E 49(5), 3641-3652 (1994).
28. F. H. Willeboordse and K. Kaneko, "Pattern dynamics of a coupled map lattice for open flow," Physica D 86(3), 428-455 (1995).
29. R. Carretero-González, "Front propagation and mode-locking in coupled map lattices," Ph.D. thesis, Queen Mary and Westfield College, London, U.K., 1997. http://www.ucl.ac.uk/~ucesrca/abstracts.html
30. V. I. Oseledec, "A multiplicative ergodic theorem. Ljapunov characteristic numbers for dynamical systems," Trans. Moscow Math. Soc. 19, 197-231 (1968).
31. P. J. Davis, Circulant Matrices (Wiley, New York, 1979).
32. R. Bellman, Introduction to matrix analysis (McGraw-Hill, New York, 1960).
33. S. Isola, A. Politi, S. Ruffo, and A. Torcini, "Lyapunov spectra of coupled map lattices," Phys. Lett. A 143(8), 365-368 (1990).
34. S. Vannitsem and C. Nicolis, "Error growth dynamics in spatially extended systems," Int. J. Bifurcation Chaos Appl. Sci. Eng. 6(12A), 2223-2235 (1996).
35. N. Parekh, V. R. Kumar, and B. D. Kulkarni, "Synchronization and control of spatiotemporal chaos using time-series data from local regions," Chaos 8, 300-306 (1998).
36. S. Barnett, Matrices: methods and applications (Oxford U.P., Oxford, 1990), p. 349.
37. G. Giacomelli and A. Politi, "Spatio-temporal chaos and localization," Europhys. Lett. 15(4), 387-392 (1991).
38. H. Furstenberg and H. Kesten, "Products of random matrices," Ann. Math. Stat. 31, 573-469 (1960).
39. R. A. Johnson, K. J. Palmer, and G. R. Sell, "Ergodic properties of linear dynamical systems," SIAM (Soc. Ind. Appl. Math.) J. Math. Anal. 18(1), 1-33 (1987).
40. M. P. Hassell, H. N. Comins, and R. M. May, "Spatial structure and chaos in insect population dynamics," Nature (London) 353, 255-258 (1991).
41. H. N. Comins, M. P. Hassell, and R. M. May, "The spatial dynamics of host-parasitoid systems," J. Anim. Ecology 61, 735-748 (1992).
42. H. B. Wilson and D. A. Rand, "Reconstructing the dynamics of unobserved variables in spatially-extended systems," Proc. R. Soc. London, Ser. B 264, 625-630 (1997).
43. P. Rohani and O. Miramontes, "Host-parasitoid metapopulations: the consequences of parasitoid aggregation on spatial dynamics and searching efficiency," Proc. R. Soc. London, Ser. B 260, 335-342 (1995).