Abstract
In the first two lectures of the summer school, I have reported the studies of spatiotemporal chaos with the use of coupled map lattices (CML). On the first lecture, I have shown some qualitative results of CMLs. Since some of the inovating features in CML modelling are not recognized, some questions and answers are listed up here, starting from the most trivial one.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
K. Kaneko, Prog. Theor. Phys. 72 (1984) 480, 74 (1985) 1033; in Dynamical Problems in Soliton Systems (Springer, 1985, ed. S. Takeno) 272-277
K. Kaneko, Ph. D. Thesis, Collapse of Tori and Genesis of Chaos in Dissipative Systems, 1983 (enlarged version is published by World Sci. Pub., 1986)
K. Kaneko, Physica 23D (1986) 436
K. Kaneko, Physica 34D (1989) 1; Europhys. Lett. 6 (1988) 193; Phys. Lett. 125 A (1987) 25
J. P. Crutchfield and K. Kaneko, “Phenomenology of Spatiotemporal Chaos”, in Directions in Chaos (World Scientific, 1987) 272
K. Kaneko, Phys. Lett. 111A (1985) 321
R.J. Deissler and K. Kaneko, Phys. Lett. 119A (1987) 397
R. J. Deissler, Phys. Lett. 120A (1984) 334: I. Waller and R. Kapral, Phys. Rev. 30A (1984) 2047: Y.Oono and S. Puri, Phys. Rev. Lett. 58 (1986)836; T. Bohr and O.B Christensen, Phys. Rev. Lett. 63 (1989) 2161
J. D. Keeler and J. D. Farmer, Physica 23D (1986) 413
H. Chate and P. Manneville, Europhys. Lett. 6 (1988) 59; Physica 32D (1988) 409
J.P. Crutchfield and K. Kaneko, Phys. Rev. Lett. 60 (1988) 2715
L.A. Bunimovich and Ya.G. Sinai, Nonlinearity 1 (1989) 491
G. Mayer-Kress and K. Kaneko, J. Stat. Phys., 54 (1989) 1489
K. Kaneko, Phys. Lett. 139A (1989) 47; J.M. Houlrik, I. Webman, and M. H. Jensen, Phys. Rev. 41A (1990) 4210
K. Kaneko, “Simulating Physics with Coupled Map Lattices” in Formation, Dynamics, and Statistics of Patterns, 1 (ed. K. Kawasaki, A. Onuki, and M. Suzuki, World. Sci. 1990)
K. Kaneko “Climbing Up Dynamical Hierarchy”, in Chaotic Hierarchy (ed. G. Baier and M. Klien, World. Sci. 1990)
K. Kaneko, Phys. Rev. Lett. 63 (1989) 219; Physica 41 D (1990) 137; Phys. Rev. Lett. 65 (1990) 1391
K. Kaneko, Prog. Theor. Phys. Suppl. 99 (1989) 263
K. Kaneko, Phys. Lett. A (1990) in press
L.D. Landau and E.M. Lifshitz, Fluid Mechanics (Pergamon, London, 1959) Chapt.3
D. Ruelle and F. Takens, Comm. Math. Phys. 20 (1971) 167; 23 (1971) 343
O.E. Rössler, Phys. Lett. 71 A (1979) 155; in Lecture Notes in Applied Math., 17 (1979) 141-156; Z. Naturforschung 38a (1983) 788
G. Nicolis and I. Prigogine, Self-Organization in Nonequilibirum Systems, (John Wiley and Sons, 1977)
S.P. Kuznetsov, Radiophysics 29 (1986) 888 ( in Russian)
H. Kook, F.H. Ling and G. Schmidt, preprint (1990)
LS. Aronson, A.V. Gaponov-Grekhov, and M.I. Rabinovich, Physica 33D (1988) 1
M.J. Feigenbaum, J. Stat. Phys. 21 (1979) 669
Y. Aizawa, I. Nishikawa, and K. Kaneko, Physica D, in press (1990)
See M.H. Jensen, Phys. Rev. Lett. 62 (1989) 1361 for an extension of open flow model in 2-dimensional intermittency, with a possible relation with Benard convection
K. Kaneko, Physica 37D (1989) 60
R. Kapral, Phys. Rev. 31A (1985) 3868
P. Grassberger, in one of the lectures given at the summer school (Como, 1990)
T. Schreiber, J. Phys. 23A (1990) 393
S. Ciliberto and P. Bigazzi, Phys. Rev. Lett. 60 (1988) 286
S. Nasuno, M. Sano, Y. Sawada, in Cooperative Dynamics in Complex Systems, (ed. H. Takayama, Springer, 1989)
F. Daviaud, M. Dubois, P. Berge, Europhys. Lett. 9 (1989) 441
J. Gollub and R. Ramshankar, in New Perspectives in Turbulence (eds. S. Orszag and L. Sirovich, Springer)
Y. Couder, in one of the lectures given at the summer school (Como, 1990)
P. Manneville, in Macroscopic Modelling of Turbulent Flows, (eds. U. Frisch et al., Lecture Notes in Physics 230; Springer, 1985)
M. Yamada and K. Ohkitani, Phys. Rev. Lett. 60 (1988) 983
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Plenum Press, New York
About this chapter
Cite this chapter
Kaneko, K. (1991). Coupled Map Lattice. In: Artuso, R., Cvitanović, P., Casati, G. (eds) Chaos, Order, and Patterns. NATO ASI Series, vol 280. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0172-2_10
Download citation
DOI: https://doi.org/10.1007/978-1-4757-0172-2_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-0174-6
Online ISBN: 978-1-4757-0172-2
eBook Packages: Springer Book Archive